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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.


Correct answer : (4)
 2.  
What is the value of x, if 2(x - 2) + 9 = 3x + 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.]


Correct answer : (2)
 3.  
Which of the following choices is the solution for the equation n (-3) = 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.]


Correct answer : (4)
 4.  
Find the value of m, if m + 41 5 = 61 7.
a.
131 35
b.
133 35
c.
21 7
d.
23 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.]


Correct answer : (2)
 5.  
Solve for y:
8y + 4 5 = 5y - 4
a.
- 8 5
b.
- 9 5
c.
9 5
d.
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.]


Correct answer : (1)
 6.  
Solve for x:
x + x13 + x8 = 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
[Add.]

x104 = 1
[Divide throughout by 125.]

x = 104
[Multiply throughout by 104.]


Correct answer : (4)
 7.  
Solve for w:
w + w2 + w6 - w3 = - 1 15
a.
1 15
b.
- 1 20
c.
1 20
d.
- 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


Correct answer : (2)
 8.  
Solve for m:
9 + 9(- m + 6) = 15m - 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.]


Correct answer : (1)
 9.  
Solve:
2x + 5 + 2(2 + 7x2) = 7(1 - x) + 14(x2 + 2)
a.
26 9
b.
27 10
c.
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.]


Correct answer : (1)
 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 = 2p + b
b.
l = p2 - b
c.
l = p2 + b
d.
l = 2p - 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


Correct answer : (2)

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