Equations with parenthesis

Equations with parentheses: decimals & fractions - Questions

Answers

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

$3 t-18=4\left(-3-\frac{3}{4} t\right)$
$3 t-18 =-12-3 t$	Distribute.
$3 t-18+3 t =-12-3 t+3 t$	Add $3t$ to each side.
$6 t-18 =-12 = 18$	Combine like terms.
$6 t-18+18 =-12+18$	Add $18$ to each side.
$6 t =6$	Combine like terms.
$\frac{6 t}{6} =\frac{6}{6}$	Divide each side by $6$ .
$t =1$	Simplify.

The answer: $t = 1$

Let's check our work!

$\begin{aligned} 3 t-18 &=4\left(-3-\frac{3}{4} t\right) \\ 3(1)-18 & \stackrel{?}{=} 4\left(-3-\frac{3}{4}(1)\right) \\ 3-18 & \stackrel{?}{=} 4\left(-3-\frac{3}{4}\right) \\ -15 & \stackrel{?}{=} 4\left(-\frac{12}{4}-\frac{3}{4}\right) \\ -15 & \stackrel{?}{=} 4\left(-\frac{15}{4}\right) \\ -15 & \stackrel{?}{=}-\frac{60}{4} \\ -15 &=-15 \text { Yes!} \end{aligned}$

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

$0.75(8b+4)−1=4b+14$
$6 b+3-1 =4 b+14$	Distribute.
$6 b+2 =4 b+14$	Combine like terms.
$6 b+2-4 b =4 b+14 - 4b$	Subtract $4b$ from each side.
$2 b + 2 = 14$	Combine like terms.
$2 b+2-2 =14-2$	Subtract $2$ from each side.
$2 b =12$	Combine like terms.
$\frac{2 b}{2} =\frac{12}{2}$	Divide each side by $2$ .
$b =6$	Simplify.

The answer: $b = 6$

Let's check our work!

$\begin{gathered} 0.75(8 b+4)-1=4 b+14 \\ 0.75(8(6)+4)-1 \stackrel{?}{=} 4(6)+14 \\ 0.75(48+4)-1 \stackrel{?}{=} 24+14 \\ 0.75(52)-1 \stackrel{?}{=} 38 \\ 39-1 \stackrel{?}{=} 38 \\ 38=38 \quad \text { Yes! } \end{gathered}$

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

$4 n+2=6\left(\frac{1}{3} n-\frac{2}{3}\right)$
$4 n+2 =2 n-4$	Distribute.
$4 n+2-2 n =2 n-4-2 n$	Subtract $2n$ from each side.
$2 n+2 =-4$	Combine like terms.
$2 n+2-2 =-4-2$	Subtract $2$ from each side.
$2 n =-6$	Combine like terms.
$\frac{2 n}{2} =\frac{-6}{2}$	Divide each side by $2$ .
$n =-3$	Simplify.

The answer: $n = -3$

Let's check our work!

$\begin{aligned} 4 n+2 &=6\left(\frac{1}{3} n-\frac{2}{3}\right) \\ 4(-3)+2 & \stackrel{?}{=} 6\left(\frac{1}{3}(-3)-\frac{2}{3}\right) \\ -12+2 & \stackrel{?}{=} 6\left(-1-\frac{2}{3}\right) \\ -10 & \stackrel{?}{=} 6\left(-\frac{5}{3}\right) \\ -10 & \stackrel{?}{=}-\frac{30}{3} \\ -10 &=-10 \text { Yes!} \end{aligned}$

4. $g = -\frac{1}{4}$

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

$12 g=12\left(\frac{2}{3} g-1\right)+11$
$12 g =8 g-12+11$	Distribute.
$12 g =8 g-1$	Combine like terms.
$12 g-8 g =8 g-1-8 g$	Subtract $8g$ from each side.
$4 g =-1$	Combine like terms.
$\frac{4 g}{4} =\frac{-1}{4}$	Divide each side by $4$ .
$g =-\frac{1}{4}$	Simplify.

The answer: $g = -\frac{1}{4}$

Let's check our work!

$\begin{aligned} 12 g &=12\left(\frac{2}{3} g-1\right)+11 \\ 12\left(-\frac{1}{4}\right) & \stackrel{?}{=} 12\left(\frac{2}{3}\left(-\frac{1}{4}\right)-1\right)+11 \\ -3 & \stackrel{?}{=} 12\left(-\frac{2}{12}-1\right)+11 \\ -3 & \stackrel{?}{=} 12\left(-\frac{2}{12}-\frac{12}{12}\right)+11 \\ -3 & \stackrel{?}{=} 12\left(-\frac{14}{12}\right)+11 \\ -3 & \stackrel{?}{=}-14+11 \\ -3 &=-3 \text { Yes!} \end{aligned}$