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Copy of Solving Equations Basics (7/21/2024)

Last updated 8 months ago
55 questions
Note from the author:

Essential Question: How do we solve algebraic equations using opposite operations?


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 using opposite operations?


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.

Day 1 8/30/23

Opposite Operations and Solving Equations

Required
5

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

Required
5

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

Required
8

Match the operation with its inverse.

Draggable itemCorresponding Item
inverse of subtraction
subtraction
inverse of multiplication
addition
inverse of addition
division
inverse of division
multiplication
Required
2

What is the first step to solve this equation?

Required
5

Solve this equation.

Required
2

What is the first step to solve this equation?

Required
5

Solve this equation




Required
2

What is the first step to solve this equation?

Required
5

Solve this equation.


Required
6

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

  1. division
  2. subtraction
  3. addition
  4. parentheses ( )
  5. exponents
  6. multiplication
Required
6

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)

  1. addition and subtraction (outside parentheses)
  2. multiplication and division (outside parentheses)
  3. parentheses ( )
Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Required
5

Solve this equation




Day 2 8/31/23

Video Notes: Solving 2-step equations


Required
4

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

  1. divide both sides of the equation by 3
  2. add 7 to both sides of the equation
  3. the result is x=7
  4. Before we start solving, we identify the variable a, so we can solve for it the variable
Required
10

Solve this equation.


Required
2

What is the first step to solving this equation?

Required
2

What is the second step to solving this equation?

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

10

Day 3 9-1-22

Spiral Review

Required
5

Translate this expression.

“eighteen less than a number”

Required
5

Translate this expression.

“twice a number plus four”

Required
5

Write each expression in words

-4x+13

Required
8

Which words or phrases have the same meaning as multiplication?

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.

1._______
2._______
3._______
Required
10

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


  1. Use distribution to multiply (7a+5) by -4 to get -28a - 20
  2. undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
  3. Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
  4. The solution is a = 5
  5. undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
Required
10

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

Required
10

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


  1. The solution is x = -4
  2. undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
  3. Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25
  4. undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
  5. Simplify like terms to get the equation -7x - 3 = 25
Required
10

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

Required
12

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



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