Unit 5: Linear Functions and Solving Equations

1. Which of the following equations will have no solution when simplified?

2. Find the value of x: 𝟒𝒙 + 𝟐(𝒙 – 𝟑) = 𝟔𝒙 – 𝟔

3. Simplify the expression: $$\frac{1}{2}(𝟒𝒙+𝟔)=−𝟓𝒙+𝟐𝟒.𝟕$$

4. A student worked the equation on the left, showing his steps. In which step did he make a mistake?

5. Find the value of x: $$\frac{x}{2}+𝟓=𝟏𝟐$$

6. Solve the equation for x: $$\frac{3}{4}+\frac{1}{2}x=x-\frac{1}{4}$$

7. Solve the equation for x:

$$−𝟏𝟎(𝒙+𝟐)−𝟓𝒙=−𝟗𝒙+𝟏𝟔$$

8. James is remodeling his home and wants to put in all hard-wood flooring. The graph on the left shows the price of hard-wood flooring per square foot. What is the unit rate per square foot of hard-wood flooring?

9. Mike and Anna are having a weight loss competition. Mike wants to practice kickboxing to burn calories while Anna prefers to run. Mike records his calories burned in the table and Anna graphs her calories burned in the graph.

Who burns more calories per hour?

10. Payton and Elizabeth are working on their keyboarding skills. Payton uses the equation below to show how many words (W) she can type per minute (m). The graph below represents how many words per minute Elizabeth can type.

Which statement below is most accurate?

14. Kinnady is applying to work at two different restaurants to earn money while she attends college. Both restaurants offer an hourly rate of pay as well as any tips she earns during her shift. The first restaurant gave their pay scale information in a table, while the second restaurant gave their information in a graph. Both are shown on the left.

Which restaurant will pay Kinnady more money per hour?

15. Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line $$\overline{AX}$$ . The slope between point C and point A is 23. What is the slope between point X and point C?

16. Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line $$\overline{AX}$$ .

Which proportional statement below is TRUE?

17. Consider the graph shown. Which statement is true about Line 1 and Line 2?

18. Given the equation $$𝒚=\frac{2}{3}𝒙+𝟒$$ , which statement below is FALSE?

19. Given the equation $$𝒚=−𝟒𝒙$$ , which statement below is TRUE?