Question

take out your notes with acceptable moves and steps. solve each equation (isolate the variable), write the acceptable moves (steps), then check (plug in) the solution to see if it is correct.

equation	acceptable moves (steps)	work to find solution	check
21 = 4y - 7
84 = 9a + 12
2(6p - 2) = 32

Explanation:

For the equation $21 = 4y-7$:

Step1: Add 7 to both sides

Adding 7 to both sides isolates the term with the variable.
$21+7 = 4y-7 + 7$
$28=4y$

Step2: Divide both sides by 4

Dividing by 4 gives the value of y.
$\frac{28}{4}=\frac{4y}{4}$
$y = 7$

Step1: Subtract 12 from both sides

To isolate the term with the variable.
$84-12=9a + 12-12$
$72=9a$

Step2: Divide both sides by 9

To solve for a.
$\frac{72}{9}=\frac{9a}{9}$
$a = 8$

Step1: Divide both sides by 2

To simplify the left - hand side.
$\frac{2(6p - 2)}{2}=\frac{32}{2}$
$6p-2 = 16$

Step2: Add 2 to both sides

To isolate the term with the variable.
$6p-2+2=16 + 2$
$6p=18$

Step3: Divide both sides by 6

To solve for p.
$\frac{6p}{6}=\frac{18}{6}$
$p = 3$

Answer:

$y = 7$
Check:
Substitute $y = 7$ into the original equation $21=4y - 7$.
$4\times7-7=28 - 7=21$. The solution is correct.

For the equation $84=9a + 12$: