# Solve Linear Equation Worksheet

Solve Linear Equation Worksheet
• Page 1
1.
A number decreased by 9 equals 4 times the number. Find the number.
 a. 4 b. 3 c. -4 d. -3

#### Solution:

Let m be the required number.

m - 9 = 4m
[Write the equation.]

m - 9 - m = 4m - m
[Subtracting m from the two sides of the equation.]

-9 = 3m
[Simplify.]

-93 = 3m3
[Divide throughout by 3.]

-3 = m

The required number is -3.

2.
What is the value of $x$, if 2($x$ - 2) + 9 = 3$x$ + 16?
 a. 11 b. -11 c. -21 d. 21

#### Solution:

2(x - 2) + 9 = 3x + 16

2x - 4 + 9 = 3x + 16
[Simplify the terms inside the brackets.]

2x + 5 - 5 = 3x + 16 - 5
[Group the like terms and simplify.]

2x = 3x + 11
[Simplify.]

2x - 3x = 3x + 11 - 3x
[Subtracting 3x from the two sides of the equation.]

-x = 11
[Simplify.]

x = -11
[Multiply with -1 on both sides.]

3.
Which of the following choices is the solution for the equation $\frac{n}{\left(-3\right)}$ = 6?
 a. 23 b. 18 c. 24 d. - 18

#### Solution:

n(-3) = 6

(- 3) × n(-3)= (- 3) × 6
[Multiply throughout by - 3.]

n = - 18
[Simplify.]

4.
Find the value of $m$, if $m$ + $4\frac{1}{5}$ = $6\frac{1}{7}$.
 a. $1\frac{31}{35}$ b. $1\frac{33}{35}$ c. $2\frac{1}{7}$ d. $2\frac{3}{35}$

#### Solution:

m + 41 / 5 = 61 / 7

m + 21 / 5 = 43 / 7
[Change to an improper fraction.]

m + 21 / 5 - 21 / 5 = 43 / 7 - 21 / 5
[Subtracting 21 / 5 from the two sides of the equation.]

m = 68 / 35
[Simplify.]

m = 133 / 35
[Change to a mixed fraction.]

5.
Solve for $y$:
8$y$ + $\frac{4}{5}$ = 5$y$ - 4
 a. - $\frac{8}{5}$ b. - $\frac{9}{5}$ c. $\frac{9}{5}$ d. $\frac{8}{5}$

#### Solution:

8y + 4 / 5 = 5y - 4

3y + 4 / 5 = - 4
[Subtract 5y from the two sides of the equation.]

3y = - 4 - 4 / 5
[Subtract 4 / 5 from the two sides of the equation.]

3y = - 24 / 5
[Simplify.]

y = - 8 / 5
[Divide throughout by 3.]

6.
Solve for $x$:
$x$ + $\frac{x}{13}$ + $\frac{x}{8}$ = 125
 a. - 103 b. 103 c. - 104 d. 104

#### Solution:

x + x13 + x8 = 125

x (1 + 1 / 8 + 1 / 13) = 125

x (104 / 104+ 13 / 104+ 8 / 104) = 125
[Write equivalent fractions for 1, 1 / 8 and 1 / 13.]

x ( 125 / 104) = 125

x104 = 1
[Divide throughout by 125.]

x = 104
[Multiply throughout by 104.]

7.
Solve for $w$:
$w$ + $\frac{w}{2}$ + $\frac{w}{6}$ - $\frac{w}{3}$ = - $\frac{1}{15}$
 a. $\frac{1}{15}$ b. - $\frac{1}{20}$ c. $\frac{1}{20}$ d. - $\frac{1}{15}$

#### Solution:

w + w2 + w6 - w3 = - 1 / 15

w (1 + 1 / 2+ 1 / 6- 1 / 3) = - 1 / 15

w ( 6 / 6 + 3 / 6 + 1 / 6 - 2 / 6 ) = - 1 / 15
[Write equivalent fractions for 1, 1 / 2, 1 / 6 and 1 / 3.]

w(8 / 6) = - 1 / 15
[Simplify.]

So, w = - 1 / 20

8.
Solve for $m$:
9 + 9(- $m$ + 6) = 15$m$ - 7(8 + $m$)
 a. 7 b. 6 c. 8 d. 9

#### Solution:

9 + 9(- m + 6) = 15m - 7(8 + m)

9 - 9m + 54 = 15m - 56 - 7m
[Use the distributive property.]

63 - 9m = 8m - 56
[Simplify.]

63 - 17m = - 56
[Subtract 8m from the two sides of the equation.]

- 17m = - 119
[Subtract 63 from the two sides of the equation.]

m = 7
[Divide throughout by - 17.]

9.
Solve:
2$x$ + 5 + 2(2 + 7$x$2) = 7(1 - $x$) + 14($x$2 + 2)
 a. $\frac{26}{9}$ b. $\frac{27}{10}$ c. $\frac{28}{9}$ d. 3

#### Solution:

2x + 5 + 2(2 + 7x2) = 7(1 - x) + 14(x2 + 2)
[Write the expression.]

2x + 5 + 4 + 14x2 = 7 - 7x + 14x2 + 28
[Distributive property.]

2x + 9 = 35 - 7x
[Subtract 14x2 from the two sides of the equation.]

9x + 9 = 35
[Add 7x to both sides of the equation.]

9x = 26
[Subtract 9 from the two sides of the equation.]

x = 26 / 9
[Divide throughout by 9.]

10.
The perimeter of a rectangle is represented by $p$ = 2($l$ + $b$) where $p$, $l$ and $b$ are the perimeter, length and width respectively. Solve for $l$.
 a. $l$ = 2$p$ + $b$ b. $l$ = $\frac{p}{2}$ - $b$ c. $l$ = $\frac{p}{2}$ + $b$ d. $l$ = 2$p$ - $b$

#### Solution:

p = 2(l + b)

p2 = l + b
[Divide throughout by 2.]

p2 - b = l
[Subtract b from the two sides of the equation.]

l = p2 - b