Equations with parenthesis

Equations with parentheses - Questions

Answers

1.

We need to manipulate the equation to get $c$ by itself.

$4(3+c)+c=c+4$
$12+4 c+c =c+4$	Distribute.
$5 c+12 =c+4$	Combine like terms.
$5 c+12-c =c+4-c$	Subtract $c$ from each side.
$4 c+12 =4$	Combine like terms.
$4 c+12-12 =4-12$	Subtract $12$ from each side.
$4 c =-8$	Combine like terms.
$\frac{4 c}{4} =\frac{-8}{4}$	Divide each side by $4$ .
$c =-2$	Simplify.

The answer: $c = -2$

Let's check our work!

$\begin{gathered} 4(3+c)+c=c+4 \\ 4(3+(-2))+(-2) \stackrel{?}{=}-2+4 \\ 4(1)-2 \stackrel{?}{=} 2 \\ 4-2 \stackrel{?}{=} 2 \\ 2=2 \quad \text { Yes! } \end{gathered}$

We need to manipulate the equation to get $p$ by itself.

$10p−3=2(12+4p)−7$
$10 p-3 =24+8 p-7$	Distribute.
$10 p-3 =17+8 p$	Combine like terms.
$10 p-3-8 p =17+8 p-8 p$	Subtract $8p$ from each side.
$2 p-3 =17$	Combine like terms.
$2 p-3+3 =17+3$	Add $3$ to each side.
$2 p =20$	Combine like terms.
$\frac{2 p}{2} =\frac{20}{2}$	Divide each side by $2$ .
$p =10$	Simplify.

The answer: $p = 10$

Let's check our work!

$\begin{aligned} 10 p-3 &=2(12+4 p)-7 \\ 10(10)-3 & \stackrel{?}{=} 2(12+4(10))-7 \\ 100-3 & \stackrel{?}{=} 2(12+40)-7 \\ 97 & \stackrel{?}{=} 2(52)-7 \\ 97 & \stackrel{?}{=} 104-7 \\ 97 &=97 \quad \text { Yes! } \end{aligned}$

We need to manipulate the equation to get $t$ by itself.

$−t=9(t−10)$
$-t =9 t-90$	Distribute.
$-t-9 t =9 t-90-9t$	Subtract $9t$ from each side.
$-10 t =-90$	Combine like terms.
$\frac{-10 t}{-10} =\frac{-90}{-10}$	Divide each side by $-10$ .
$t =9$	Simplify.

The answer is: $t = 9$

Let's check our work!

$\begin{aligned} &-t=9(t-10) \\ &-9 \stackrel{?}{=} 9(9-10) \\ &-9 \stackrel{?}{=} 9(-1) \\ &-9=-9 \quad \text { Yes! } \end{aligned}$

We need to manipulate the equation to get $g$ by itself.

$6(−2g−1)=−(13g+2)$
$-12 g-6 =-13 g-2$	Distribute.
$-12 g-6+12 g =-13 g+12 g-2$	Add $12g$ to each side.
$-6+2 =-g-2+2$	Add $2$ to each side.
$-4 =-g$	Divide by $-1$ .
$4 =g$	Combine like terms.

The answer: $g = 4$

Let's check our work!

$\begin{aligned} 6(-2 g-1) &=-(13 g+2) \\ 6(-2(4)-1) & \stackrel{?}{=}-(13(4)+2) \\ 6(-8-1) & \stackrel{?}{=}-(52+2) \\ 6(-9) & \stackrel{?}{=}-(54) \\ -54 &=-54 \quad \text { Yes! } \end{aligned}$