Question

5-4 hw: solving two-step equations
name:
date:
period:
directions: solve each equation using the steps discussed in class.
then check your answers with the necessary steps.
you must show your work in order to receive full credit.

1. $4y + 1 = 13$

check:

1. $7 = - 3c - 2$

check:

1. $\frac{r}{2} + 6 = 11$

check:

1. $2 = \frac{1}{-8}x - 7$

check:

Explanation:

1) Equation: $4y + 1 = 13$

Step1: Subtract 1 from both sides

$4y + 1 - 1 = 13 - 1$
$4y = 12$

Step2: Divide by 4 on both sides

$\frac{4y}{4} = \frac{12}{4}$
$y = 3$

Check Step1: Substitute $y=3$

$4(3) + 1 = 13$
$12 + 1 = 13$
$13 = 13$

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2) Equation: $7 = -3c - 2$

Step1: Add 2 to both sides

$7 + 2 = -3c - 2 + 2$
$9 = -3c$

Step2: Divide by -3 on both sides

$\frac{9}{-3} = \frac{-3c}{-3}$
$c = -3$

Check Step1: Substitute $c=-3$

$7 = -3(-3) - 2$
$7 = 9 - 2$
$7 = 7$

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3) Equation: $\frac{r}{2} + 6 = 11$

Step1: Subtract 6 from both sides

$\frac{r}{2} + 6 - 6 = 11 - 6$
$\frac{r}{2} = 5$

Step2: Multiply by 2 on both sides

$\frac{r}{2} \times 2 = 5 \times 2$
$r = 10$

Check Step1: Substitute $r=10$

$\frac{10}{2} + 6 = 11$
$5 + 6 = 11$
$11 = 11$

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4) Equation: $2 = \frac{1}{-8}x - 7$

Step1: Add 7 to both sides

$2 + 7 = \frac{1}{-8}x - 7 + 7$
$9 = -\frac{1}{8}x$

Step2: Multiply by -8 on both sides

$9 \times (-8) = -\frac{1}{8}x \times (-8)$
$x = -72$

Check Step1: Substitute $x=-72$

$2 = \frac{1}{-8}(-72) - 7$
$2 = 9 - 7$
$2 = 2$

Answer:

1. $y = 3$
2. $c = -3$
3. $r = 10$
4. $x = -72$