Equations with variables on both sides: decimals & fractions - Questions

Answers

1. k = 3

We need to manipulate the equation to get k by itself.

4.5+1.5k=18−3k
4.5+1.5 k+3 k =18-3 k+3 k Add 3k to each side.
4.5 k+4.5 =18 Combine like terms.
4.5 k+4.5-4.5 =18-4.5 Subtract 4.5 from each side.
4.5 k =13.5 Combine like terms.
\frac{4.5 k}{4.5} =\frac{13.5}{4.5} Divide each side by 4.5.
k =3 Simplify.


The answer: k = 3


Let's check our work!

\begin{aligned} 4.5+1.5 k &=18-3 k \\ 4.5+1.5(3) & \stackrel{?}{=} 18-3(3) \\ 4.5+4.5 & \stackrel{?}{=} 18-9 \\ 9 &=9 \quad \text { Yes! } \end{aligned}


2.

We need to manipulate the equation to get s by itself.

2-2 s=\frac{3}{4} s+13
2-2 s-\frac{3}{4} s =\frac{3}{4} s+13-\frac{3}{4} s Subtract \frac{3}{4} from each side.
-\frac{11}{4} s+2 =13 Combine like terms.
-\frac{11}{4} s+2-2 =13-2 Subtract 2 from each side.
-\frac{11}{4} s =11 Combine like terms.
s \cdot\left(-\frac{4}{11}\right) =11 \cdot\left(-\frac{4}{11}\right) Multiply each side by -\frac{4}{11}.
s =-\frac{44}{11}
s =-4 Simplify.


The answer: s = -4


Let's check our work!

\begin{aligned} 2-2 s &=\frac{3}{4} s+13 \\ 2-2(-4) & \stackrel{?}{=} \frac{3}{4}(-4)+13 \\ 2+8 & \stackrel{?}{=}-\frac{12}{4}+13 \\ 10 & \stackrel{?}{=}-3+13 \\ 10 &=10 \quad \text { Yes! } \end{aligned}


3. g = 0.5

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

9+3.5g=11−0.5g
9+3.5 g+0.5 g =11-0.5 g+0.5 g Add 0.5g to each side.
9+4 g =11 Combine like terms.
4 g+9-9 =11-9 Subtract 9 from each side.
4 g =2 Combine like terms.
\frac{4 g}{4} =\frac{2}{4} Divide each side by 4.
g =0.5 Simplify.


The answer: g = 0.5


Let's check our work!

\begin{aligned} 9+3.5 g &=11-0.5 g \\ 9+3.5(0.5) & \stackrel{?}{=} 11-0.5(0.5) \\ 9+1.75 & \stackrel{?}{=} 11-0.25 \\ 10.75 &=10.75 \quad \text { Yes! } \end{aligned}


4. p = 3

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

16-3 p=\frac{2}{3} p+5
16-3 p-\frac{2}{3} p =\frac{2}{3} p+5-\frac{2}{3} p Subtract \frac{2}{3}p from each side.
-\frac{11}{3} p+16 =5 Combine like terms.
-\frac{11}{3} p+16-16 =5-16 Subtract 16 from each side.
-\frac{11}{3} p =-11 Combine like terms.
-\frac{11}{3} p \cdot\left(-\frac{3}{11}\right) =-11 \cdot\left(-\frac{3}{11}\right) Multiply each side by -\frac{3}{11}
p =\frac{33}{11}
p =3 Simplify.


The answer: p = 3


Let's check our work!

\begin{aligned} 16-3 p &=\frac{2}{3} p+5 \\ 16-3(3) & \stackrel{?}{=} \frac{2}{3}(3)+5 \\ 16-9 & \stackrel{?}{=} 2+5 \\ 7 &=7 \quad \text { Yes! } \end{aligned}