# 3.01 Solving linear equations

Worksheet
Equations with brackets
1

Solve the following equations:

a
4 \left(x + 4\right) = 24
b
5 \left( 3 x + 6\right) = 78
c
5 \left( 2 x - 4\right) = - 70
d
2\left(x+5\right)=16
e
6\left(2x-4\right)=-84
f
3\left(x+1\right)+2=-1
g
-2\left(x+2\right)-4=4
h
3\left(x-1\right)-5=-11
2

Solve the following equations:

a
3 \left( 6 x - 7\right) - 5 x + 8 = 26
b
2 \left( 3 x - 5\right) + 3 \left( 4 x + 6\right) = 62
c
- 3 \left( 2 x - 5\right) + 5 \left( 3 x + 4\right) = 53
d
6\left(5x-8\right)-3x+7=40
e
2\left(4x-5\right)+3\left(2x+6\right)=36
f
3\left(x+6\right)+3\left(x+24\right)=12
g
3\left(x-1\right)-5=-8.6
h
3.8\left(x+4\right)-2=1.8
i
3\left(x+\dfrac{3}{2}\right)+3=-\dfrac{15}{2}
j
2.2\left(x+3\right)-4=-8.4
Equations with fractions
3

Solve the following equations:

a
\dfrac{x}{6} = \dfrac{5}{3}
b
\dfrac{x}{9} = 2\dfrac{2}{3}
c
\dfrac{2}{2.5} = \dfrac{7}{x}
d
x + \dfrac{2 x - 4}{4} = 3
e
x + \dfrac{4 x + 5}{6} = 2
f
\dfrac{7}{9} = \dfrac{8}{x}
g
x+\dfrac{5x-5}{6}=1
h
x+\dfrac{4x+2}{6}=5
4

Solve the following equations:

a
\dfrac{8.4}{7.5} = \dfrac{x}{5}
b
\dfrac{x}{5}+\dfrac{x}{2} = 21
c
\dfrac{x}{2} - \dfrac{x}{5} = - 12
d
\dfrac{- x}{4} + \dfrac{x}{3} = - 5
e
\dfrac{- x}{2} - \dfrac{x}{3} = - 5
f
\dfrac{3 x}{2} + \dfrac{7 x}{5} = 5
g
\dfrac{5 x}{6} - \dfrac{3 x}{7} = - 2
h
\dfrac{2 x - 3}{6} - \dfrac{3 x - 2}{5} = - 5
i
\dfrac{5 x - 4}{5} - \dfrac{3 x - 6}{4} = 3
j
\dfrac{6x-6}{2}-\dfrac{3x-3}{5}=-4
Equations with pronumerals on both sides
5

Solve the following equations:

a
3 x = x + 10
b
3 x = - 4 x - 35
c
12x - 8 = -4x
d
27 + 7x = -2x
e
10+4x = -11x -20
f
28 - 3x = 11 + 14x
g
5x+22 = 8 - 2x
h
4 x - 3 = - 8 x + 57
6

Solve the following equations:

a
3 x + 6 = 3 \left( 5 x - 4\right) + 42
b
4x+6=7\left(5x-4\right)+96
c
16x -7 = 4 \left(9x -7\right) -19
d
10x - 12 = 2 \left(10x - 5\right) + 38
e
7 \left( 8 x + 4\right) = 3 \left( 3 x + 7\right) + 195
f
3 \left(8 + 2x \right) = 6 \left(4 - 2x\right) +3
g
7 \left(x - 8 \right) = 4 \left(3x +5\right) +24
h
5 \left(6x + 7 \right) = 25x +2 \left(11 -4x\right)
7

Solve the following equations:

a
\dfrac{3 x - 7}{8} = - 5 x + 26
b
\dfrac{4 x - 51}{7} = 3 x
c
\dfrac{- 4 x + 57}{3} = 5 x
d
\dfrac{5 x}{4} - 6 = \dfrac{2 x}{7}
e
\dfrac{6 x}{2} + 2 = \dfrac{3 x}{5}
f
\dfrac{8 x}{4} - 2 = \dfrac{7 x}{3} + 4
g
\dfrac{7 x}{3} + 3 = \dfrac{9 x}{4} + 3
h
\dfrac{6 x - 2}{3} = \dfrac{5 x - 3}{4}
i
\dfrac{7 x + 2}{3} = \dfrac{5 x + 9}{4}
j
\dfrac{5 x + 4}{7} = \dfrac{- 3 x + 12}{3}
k
\dfrac{x + 5}{x + 2} = \dfrac{x + 8}{x + 6}
l
\dfrac{3x-5}{8}=\dfrac{-2x-4}{5}