Illustrative Math - Algebra 1 - Unit 2- Lesson 19

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11 Questions
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1.
Here is an inequality: \frac{7x+6}{2}\leq3x+2

Select all of the values that are a solution to the inequality.
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2.
Find the solution set to this inequality: 2x-3>\frac{2x-5}{2}
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3.
Here is an inequality: \frac{-10+x}{4}+5\leq \frac{7x-5}{3}
What value of x will produce equality (or make the two sides equal)?
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4.
Noah is solving the inequality 7x+5>2x+35. First, he solves the equation 7x+5=2x+35 and gets x=6.

How does the solution to the equation 7x+5=2x+35 help Noah solve the inequality 7x+5>2x+35?Explain your reasoning.
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5.
Which graph represents the solution to 5+8x<3(2x+4)?
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6.
Solve this system of linear equations without graphing:
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9.
How many solutions does this system of equations have? Explain how you know.
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10.
The principal of a school is hosting a small luncheon for her staff. She plans to prepare two sandwiches for each person. Some staff members offer to bring salads and beverages.

The principal has a budget of $225 and expects at least 16 people to attend. Sandwiches cost $3 each.

Select all of the equations and inequalities that could represent the constraints in the situation, where n is number of people attending and s is number of sandwiches.
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11.
Students at the college are allowed to work on campus no more than 20 hours per week. The jobs that are available pay different rates, starting from $8.75 an hour. Students can earn a maximum of $320 per week.

Write at least two inequalities that could represent the constraints in this situation. Be sure to specify what your variables represent.
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This lesson is from Illustrative Mathematics. Algebra 1, Unit 2, Lesson 19. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/1/2/19/index.html ; accessed 26/July/2021.

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