Lesson 1 Cafeteria Actions and Reactions Develop Understanding

Ready

Graph the following equations on the coordinate grid. Determine if the given point is a solution to the equation.

1.

$y = 5 x - 2$

Point: $(1, 3)$ Yes/No?

2.

$y = - \frac{1}{2} x + 8$

Point: $(0, 7)$ Yes/No?

3.

$y = - x + 4$

Point: $(2, 2)$ Yes/No?

4.

$y = x + 2$

Point: $(1, 3)$ Yes/No?

5.

$y = \frac{5}{2} x - 7$

Point: $(2, - 2)$ Yes/No?

6.

$y = - \frac{4}{3} x$

Point: $(2, - 5)$ Yes/No?

Set

For each of the equations provided below, identify the first operation performed on the variable and also identify the last operation performed on the variable. Then, determine the first step that would take place when solving and the last step that would take place when solving. If needed, solve and check your solution.

7.

$3 (x - 8) + 7 = 28$

First operation to $x$ :	First step for solving:
Last operation to $x$ :	Last step for solving:

8.

$4 n - 12 = 28$

First operation to $n$ :	First step for solving:
Last operation to $n$ :	Last step for solving:

9.

$\frac{2 t + 8}{3} = 8$

First operation to $t$ :	First step for solving:
Last operation to $t$ :	Last step for solving:

10.

$5 (\frac{2}{3} k - 8) = 40$

First operation to $k$ :	First step for solving:
Last operation to $k$ :	Last step for solving:

Solve each equation and check your solution.

11.

$36 = 3 x - 6$

12.

$9 (2 n + 5) - 12 = 51$

13.

$\frac{4 (b - 2)}{5} = 8$

14.

$7 x + 13 = 62$

15.

$4 (x - 5) + 2 = 18$

16.

$- 5 x - 12 = 48$

Go

Indicate whether the given value is a solution to the corresponding equation. Show your work.

17.

$a = - 3$ : Yes/No?

$4 a + 3 = - 9$

18.

$x = \frac{4}{3}$ : Yes/No?

$\frac{3}{4} x + \frac{1}{2} = \frac{3}{2}$

19.

$y = 2$ : Yes/No?

$2.5 y - 10 = - 0.5$

20.

$z = - 5$ : Yes/No?

$2 (5 - 2 z) = 20 - 2 (z - 1)$