solving equations with variables on both sides Worksheet - Free Printable

Here are the solutions for all the problems in Sections D, E, and F.

Section D

*To solve these, divide the number on the right by the number next to $x$.*

1) $2x = 6 \rightarrow x = 3$
2) $5x = 10 \rightarrow x = 2$
3) $4x = 12 \rightarrow x = 3$
4) $10x = 90 \rightarrow x = 9$
5) $3x = 15 \rightarrow x = 5$
6) $6x = 24 \rightarrow x = 4$
7) $7x = 35 \rightarrow x = 5$
8) $12x = 36 \rightarrow x = 3$
9) $15x = 30 \rightarrow x = 2$
10) $20x = 40 \rightarrow x = 2$
11) $40x = 120 \rightarrow x = 3$
12) $50x = 200 \rightarrow x = 4$

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Section E

*To solve these, multiply the two numbers together.*

1) $\frac{x}{3} = 4 \rightarrow x = 12$
2) $\frac{x}{2} = 8 \rightarrow x = 16$
3) $\frac{x}{5} = 7 \rightarrow x = 35$
4) $\frac{x}{8} = 4 \rightarrow x = 32$
5) $\frac{x}{7} = 3 \rightarrow x = 21$
6) $\frac{x}{5} = 4 \rightarrow x = 20$
7) $\frac{x}{2} = 9 \rightarrow x = 18$
8) $\frac{x}{9} = 5 \rightarrow x = 45$
9) $\frac{x}{7} = 8 \rightarrow x = 56$
10) $\frac{x}{12} = 6 \rightarrow x = 72$
11) $\frac{x}{14} = 2 \rightarrow x = 28$
12) $\frac{x}{30} = 5 \rightarrow x = 150$

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Section F

*Mix of multiplication, division, addition, and subtraction.*

1) $4x = 48 \rightarrow x = 12$
2) $x + 13 = 22 \rightarrow x = 9$ *(Subtract 13 from 22)*
3) $9x = 63 \rightarrow x = 7$
4) $11x = 132 \rightarrow x = 12$
5) $12 + x = 26 \rightarrow x = 14$ *(Subtract 12 from 26)*
6) $\frac{x}{8} = 12 \rightarrow x = 96$ *(Multiply 12 by 8)*
7) $x - 19 = 30 \rightarrow x = 49$ *(Add 19 to 30)*
8) $10x = 160 \rightarrow x = 16$
9) $13 + x = 27 \rightarrow x = 14$ *(Subtract 13 from 27)*
10) $6x = 42 \rightarrow x = 7$
11) $x + 17 = 42 \rightarrow x = 25$ *(Subtract 17 from 42)*
12) $\frac{x}{11} = 11 \rightarrow x = 121$ *(Multiply 11 by 11)*
13) $7x = 56 \rightarrow x = 8$
14) $18 + x = 24 \rightarrow x = 6$ *(Subtract 18 from 24)*
15) $\frac{x}{4} = 12 \rightarrow x = 48$ *(Multiply 12 by 4)*
16) $25 + x = 39 \rightarrow x = 14$ *(Subtract 25 from 39)*
17) $5x = 100 \rightarrow x = 20$
18) $\frac{x}{3} = 300 \rightarrow x = 900$ *(Multiply 300 by 3)*
19) $x + 49 = 110 \rightarrow x = 61$ *(Subtract 49 from 110)*
20) $100x = 6500 \rightarrow x = 65$

Final Answer:
Section D: 1) 3, 2) 2, 3) 3, 4) 9, 5) 5, 6) 4, 7) 5, 8) 3, 9) 2, 10) 2, 11) 3, 12) 4
Section E: 1) 12, 2) 16, 3) 35, 4) 32, 5) 21, 6) 20, 7) 18, 8) 45, 9) 56, 10) 72, 11) 28, 12) 150
Section F: 1) 12, 2) 9, 3) 7, 4) 12, 5) 14, 6) 96, 7) 49, 8) 16, 9) 14, 10) 7, 11) 25, 12) 121, 13) 8, 14) 6, 15) 48, 16) 14, 17) 20, 18) 900, 19) 61, 20) 65