1.5 Solving Equations Basics (Original)

Last updated 3 months ago

48 questions

Note from the author:

Instructions

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5

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Library

1.5 Solving Equations Basics (Original)

Last updated 3 months ago

48 questions

Note from the author:

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Instructions

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Required

5

Vocabulary: In your own words, what does it mean to isolate a variable?

A.CED.1

A.REI.3

Required

5

Vocabulary: In your own words, what is an inverse operation?

A.CED.1

A.REI.3

Required

8

Draggable item		Corresponding Item

Required

2

Required

5

Solve this equation.

Required

2

Required

5

Solve this equation.

Required

2

Required

5

Solve this equation.

Required

6

Required

6

Day 2 

Video Notes: Solving 2-step equations

Required

4

Required

10

Solve this equation.

Required

2

Required

2

Required

10

Solve this equation.

Required

10

Solve this equation.

17 + 3k = 26

10

Solve this equation.

4b - 5 = -33

10

Solve this equation.

8 + 9c = - 10

10

Solve this equation.

12y + 25 = - 35

10

Solve this equation.

15h - 9 = - 54

10

Solve this equation.

8 - 10x = - 32

10

Solve this equation.

- 16 - 2j = - 34

10

Solve this equation.

10

Solve this equation.

10

Solve this equation.

10

Solve this equation.

The examples below are different in that the multiplication/division is done FIRST, followed by the addition/subtraction.

10

Solve this equation.

10

Day 3                       9-1-22

Spiral Review

Required

5

Translate this expression.

“eighteen less than a number”

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5

Translate this expression.

“twice a number plus four”

Required

5

Write each expression in words

-4x+13

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8

Required

10

Directions: Give the perimeter of each figure as a simplified expression.

Required

10

Evaluate each expression using the variable replacements.

Required

10

The expression 6x² gives the surface area of a cube, where x is the length of one side of the cube. Find the surface area of a cube with a side length of 5 meters. (Be sure to use the correct unit in your answer)

Solving Multi-Step Equations

Required

5

Use your notes from page 5 to list the 3 steps you use to solve multi-step equations.

_______ 
_______ 
_______ 

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10

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10

Solve this multi-step equation. Show your work (SYW)

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10

Required

10

Solve this multi-step equation. Show your work (SYW)

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12

Required

10

Solve this multi-step equation. Show your work (SYW)

Required

10

Solve this multi-step equation. Show your work (SYW)

Required

10

Solve this multi-step equation. Show your work (SYW)

Required

10

Solve this multi-step equation. Show your work (SYW)

Required

10

Solve this multi-step equation. Show your work (SYW)

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Required

5

Vocabulary: In your own words, what does it mean to isolate a variable?

A.CED.1

A.REI.3

Required

5

Vocabulary: In your own words, what is an inverse operation?

A.CED.1

A.REI.3

Match the operation with its inverse.

Draggable item		Corresponding Item
inverse of multiplication		subtraction
inverse of division		addition
inverse of subtraction		division
inverse of addition		multiplication

What is the first step to solve this equation?

add 8 to both sides of the equation

subtract 14 to both sides of the equation

subtract 8 to both sides of the equation

add 14 to both sides of the equation

Solve this equation.

What is the first step to solve this equation?

divide both sides by 10

multiply both sides by 10

divide both sides by 15

multiply both sides by 15

Solve this equation.

What is the first step to solve this equation?

multiply both sides by 19

divide both sides by 3

multiply both sides by 3

divide both sides by 19

Solve this equation.

Put these operations in the order by which you perform them to simplify an expression. (first to last)

parentheses ( )
subtraction
exponents
multiplication
division
addition

To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order.

Put these operations in the order by which you perform them to solve an equation. (first to last)

parentheses ( )
addition and subtraction (outside parentheses)
multiplication and division

Day 2 

Video Notes: Solving 2-step equations

Put the steps to solving this equation in the right order.

Before we start solving, we identify the variable a, so we can solve for it the variable
add 7 to both sides of the equation
divide both sides of the equation by 3
the result is x=7

Solve this equation.

What is the first step to solving this equation?

multiplying both sides of the equation by 4

subtracting both sides of the equation by 11

dividing both sides of the equation by 4

subtraction both sides of the equation by 3

What is the second step to solving this equation?

subtraction both sides of the equation by 3

dividing both sides of the equation by 4

multiplying both sides of the equation by 4

subtracting both sides of the equation by 11

Solve this equation.

Solve this equation.

17 + 3k = 26

Solve this equation.

4b - 5 = -33

Solve this equation.

8 + 9c = - 10

Solve this equation.

12y + 25 = - 35

Solve this equation.

15h - 9 = - 54

Solve this equation.

8 - 10x = - 32

Solve this equation.

- 16 - 2j = - 34

Solve this equation.

The examples below are different in that the multiplication/division is done FIRST, followed by the addition/subtraction.

Solve this equation.

Day 3                       9-1-22

Spiral Review

Translate this expression.

“eighteen less than a number”

Translate this expression.

“twice a number plus four”

Write each expression in words

-4x+13

Which words or phrases have the same meaning as multiplication?

Directions: Give the perimeter of each figure as a simplified expression.

Evaluate each expression using the variable replacements.

The expression 6x² gives the surface area of a cube, where x is the length of one side of the cube. Find the surface area of a cube with a side length of 5 meters. (Be sure to use the correct unit in your answer)

Solving Multi-Step Equations

Use your notes from page 5 to list the 3 steps you use to solve multi-step equations.

_______ 
_______ 
_______ 

Put the steps in the correct order to solve this multistep equation.

undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
The solution is a = 5
Use distribution to multiply (7a+5) by -4 to get -28a - 20
Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5

Solve this multi-step equation. Show your work (SYW)

Put the steps in the correct order to solve this multistep equation.

undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
The solution is x = -4
undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
Simplify like terms to get the equation -7x - 3 = 25
Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25

Solve this multi-step equation. Show your work (SYW)

Put the steps in the correct order to solve this multistep equation.

Use distribution to multiply (5k-3) by 2 to get 3k+10k-6=7
Check the solution by evaluating the original expression 3k+2(5k-3) to verify that it equals 7
Simplify like terms to get the equation 13k - 6 = 7
The solution is k = 1
undo subtract 6 by adding 6 to both sides of the equations to get 13k = 13
undo multiplying by 13 by dividing by both sides of the equation by 13 to get k = 1

Solve this multi-step equation. Show your work (SYW)

Match the operation with its inverse.

inverse of multiplication

subtraction

inverse of division

addition

inverse of subtraction

division

inverse of addition

multiplication

What is the first step to solve this equation?

add 8 to both sides of the equation

subtract 14 to both sides of the equation

subtract 8 to both sides of the equation

add 14 to both sides of the equation

What is the first step to solve this equation?

divide both sides by 10

multiply both sides by 10

divide both sides by 15

multiply both sides by 15

What is the first step to solve this equation?

multiply both sides by 19

divide both sides by 3

multiply both sides by 3

divide both sides by 19

Put these operations in the order by which you perform them to simplify an expression. (first to last)

parentheses ( ) 

subtraction

exponents

multiplication

division

addition

To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order. 

Put these operations in the order by which you perform them to solve an equation. (first to last)

parentheses ( ) 

addition and subtraction (outside parentheses)

multiplication and division

Put the steps to solving this equation in the right order.

Before we start  solving, we identify the variable a, so we can solve for it the variable

add 7 to both sides of the equation

divide both sides of the equation by 3

the result is x=7

What is the first step to solving this equation?

multiplying both sides of the equation by 4

subtracting both sides of the equation by 11

dividing both sides of the equation by 4

subtraction both sides of the equation by 3

What is the second step to solving this equation?

subtraction both sides of the equation by 3

dividing both sides of the equation by 4

multiplying both sides of the equation by 4

subtracting both sides of the equation by 11

Which words or phrases have the same meaning as multiplication? 

___ groups of ___

product

together

less than

more than

of

plus

times

divide

minus

total

Put the steps in the correct order to solve this multistep equation.

undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140

The solution is a = 5 

Use distribution to multiply (7a+5) by -4 to get -28a - 20

Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160

undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5

Put the steps in the correct order to solve this multistep equation.

undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28

The solution is x = -4

undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4

Simplify like terms to get the equation -7x - 3 = 25

Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25

Put the steps in the correct order to solve this multistep equation.

Use distribution to multiply (5k-3) by 2 to get 3k+10k-6=7

Check the solution by evaluating the original expression 3k+2(5k-3) to verify that it equals 7

Simplify like terms to get the equation 13k - 6 = 7

The solution is k = 1

undo subtract 6 by adding 6 to both sides of the equations to get 13k = 13

undo multiplying by 13 by dividing by both sides of the equation by 13 to get k = 1

1.5 Solving Equations Basics (Original)

1.5 Solving Equations Basics (Original)

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Vocabulary: In your own words, what does it mean to isolate a variable?

Vocabulary: In your own words, what is an inverse operation?

Solve this equation.

Solve this equation.

Solve this equation.

Day 2

Video Notes: Solving 2-step equations

Solve this equation.

Solve this equation.

Solve this equation.17 + 3k = 26

Solve this equation.4b - 5 = -33

Solve this equation.8 + 9c = - 10

Solve this equation.12y + 25 = - 35

Solve this equation.15h - 9 = - 54

Solve this equation.8 - 10x = - 32

Solve this equation.- 16 - 2j = - 34

Solve this equation.

Solve this equation.

Solve this equation.

Solve this equation.

The examples below are different in that the multiplication/division is done FIRST, followed by the addition/subtraction.

Solve this equation.

Day 3 9-1-22

Spiral Review

Translate this expression.“eighteen less than a number”

Translate this expression.“twice a number plus four”

Write each expression in words-4x+13

Directions: Give the perimeter of each figure as a simplified expression.

Evaluate each expression using the variable replacements.

The expression 6x² gives the surface area of a cube, where x is the length of one side of the cube. Find the surface area of a cube with a side length of 5 meters. (Be sure to use the correct unit in your answer)

Solving Multi-Step Equations

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Solve this multi-step equation. Show your work (SYW)

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Essential Question: How do we solve algebraic equations with more than 1-step?

Learning Target: Students will be able to solve algebraic equations representing real-world situations that involve multiple steps to solve.

Complete the entire assignment and show work for full credit.

Vocabulary: In your own words, what does it mean to isolate a variable?

Vocabulary: In your own words, what is an inverse operation?

Match the operation with its inverse.

What is the first step to solve this equation?

Solve this equation.

What is the first step to solve this equation?

Solve this equation.

What is the first step to solve this equation?

Solve this equation.

Put these operations in the order by which you perform them to simplify an expression. (first to last)

To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order. Put these operations in the order by which you perform them to solve an equation. (first to last)

Day 2

Video Notes: Solving 2-step equations

Put the steps to solving this equation in the right order.

Solve this equation.

What is the first step to solving this equation?

What is the second step to solving this equation?

Solve this equation.

Solve this equation.17 + 3k = 26

Solve this equation.4b - 5 = -33

Solve this equation.8 + 9c = - 10

Solve this equation.12y + 25 = - 35

Solve this equation.15h - 9 = - 54

Solve this equation.8 - 10x = - 32

Solve this equation.- 16 - 2j = - 34

Solve this equation.

Solve this equation.

Solve this equation.

Solve this equation.

17 + 3k = 26

Solve this equation.

4b - 5 = -33

Solve this equation.

8 + 9c = - 10

Solve this equation.

12y + 25 = - 35

Solve this equation.

15h - 9 = - 54

Solve this equation.

8 - 10x = - 32

Solve this equation.

- 16 - 2j = - 34

Translate this expression.

“eighteen less than a number”

Translate this expression.

“twice a number plus four”

Write each expression in words

-4x+13

To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order.

Put these operations in the order by which you perform them to solve an equation. (first to last)

Solve this equation.

17 + 3k = 26

Solve this equation.

4b - 5 = -33

Solve this equation.

8 + 9c = - 10

Solve this equation.

12y + 25 = - 35

Solve this equation.

15h - 9 = - 54

Solve this equation.

8 - 10x = - 32

Solve this equation.

- 16 - 2j = - 34

Translate this expression.

“eighteen less than a number”

Translate this expression.

“twice a number plus four”

Write each expression in words

-4x+13