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}


2. p = 10

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}


3. t = 9

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}


4. g = 4

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}