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Linear(Simple) Equations: Problems with Solutions
Problem 1
Find the solution
n
to the equation
n + 2 = 6
Solution:
By substracting 2 from both sides, we get
n + 2 - 2 = 6 - 2
,
or
n = 4
Problem 2
Solve the equation
z - 5 = 6
.
Solution:
By adding
5
to both sides, we get
z=5+6
, or
z=11
.
Problem 3
Solve the equation
5 - t = 0
.
Solution:
We add
t
to both sides of the equation, and we get
5-t+t=0+t
, or
t=5
.
Problem 4
Solve the equation:
n + 7=13
Solution:
By substracting 7 from both sides, we get
n+7-7=13-7
, or
n=6
.
Problem 5
Solve the equation [tex]x+34=82[/tex]
Solution:
[tex]x=82-34=48[/tex]
Problem 6
Solve the linear equation
3-a=2a
.
Solution:
By adding
a
to both sides, we get
3-a+a=2a+a
, or
3a=3
. The we divide both sides by 3 to reach the final answer,
a=1
.
Problem 7
Solve the linear equation [tex]2x-20=10[/tex]
Solution:
[tex]2x=10+20[/tex]
[tex]2x=30[/tex]
[tex]x=15[/tex]
Problem 8
Solve the equation [tex]20 - 2x = 18[/tex]
Solution:
[tex]20 - 2x = 18[/tex]
[tex]20 - 18 = 2x[/tex]
[tex]2=2x[/tex]
[tex]x=1[/tex]
Problem 9
Find
c
, if [tex]5c - 2 = 33[/tex].
Solution:
We add 2 to both sides and get
5c-2+2=33+2
, or
5c=35
. We divide both sides by 5 in order to get
c=7
.
Problem 10
Solve the equation [tex]4x=72[/tex]
Solution:
We divide both sides of the equation with 4:
[tex]\frac{4x}{4}=\frac{72}{4}[/tex]
[tex]x=18[/tex]
Problem 11
Solve the equation [tex]13x-15=24[/tex]
Solution:
[tex]13x=24+15[/tex]
[tex]13x=39[/tex]
[tex]x=3[/tex]
Problem 12
Find the solution b to the equation [tex]\frac{b}{3}=3[/tex].
Solution:
We multiply both sides of the equation by
3
in order to get [tex]\frac{b}{3}\cdot3=3\cdot3[/tex], or
b=9
.
Problem 13
Solve the linear equation [tex]2x+2=40[/tex]
Solution:
[tex]2x=40-2[/tex]
[tex]2x=38[/tex]
[tex]x=19[/tex]
Problem 14
Solve the equation
3x + 1 = 16
.
Solution:
By substracting 1 from both sides, we get
3x+1-1=16-1
, or
3x=15
. We divide both sides by 3 in order to get the value for x:
x=5
.
Problem 15
Solve the equation
2x + 5 = 9
Solution:
By substracting 5 from both sides of the equation, we get
2x+5-5=9-5
, or
2x=4
. Then we divide both sides by 2 to reach the solution, [tex]x=2[/tex].
Problem 16
Solve the equation
m+10=3m
.
Solution:
By substracting
m
from both sides, we get
m+10-m=3m-m
, so
10=2m
or
2m=10
. Dividing both sides of the equation by 2, we find that
m=5
Problem 17
Solve the linear equation [tex]19z=38+6\times 19[/tex]
Solution:
We divide both sides by 19:
[tex]\frac{19z}{19}=\frac{38}{19}+6\cdot\frac{19}{19}[/tex]
[tex]z=2+6[/tex]
[tex]z=8[/tex]
Problem 18
Find the solution
y
to the linear equation
2y+6=y+11
.
Solution:
First, we substract
6
from both sides to get
2y+6-6=y+11-6
, or
2y=y+5
.
Then we substract
y
from both sides to reach the final solution,
y=5
.
Problem 19
Solve the equation [tex]\frac{1}{x}=\frac{1}{5}[/tex]
Solution:
The equation is defined for [tex]x \ne 0[/tex]. We cross multiply and get
[tex]x=5[/tex], which is a valid value for
x
and the solution.
Problem 20
Find the solution
x
to the equation [tex]x-1+x-2+x-3=0[/tex]
Solution:
[tex]x+x+x-1-2-3=0[/tex]
[tex]3x-6=0[/tex]
[tex]3x=6[/tex]
[tex]x=2[/tex]
Problem 21
Find the solution
y
to the equation [tex]y+10=13y-74[/tex]
Solution:
[tex]10+74=13y-y[/tex]
[tex]12y=84[/tex]
[tex]y=7[/tex]
Problem 22
Solve the equation
3c=8c
.
Solution:
We substract
3c
from both sides of the equation to get
3c-3c=8c-3c
, or
5c=0
. The we divide both sides by 5 and the answer is
c=0
.
Problem 23
Solve the linear equation [tex]\frac{3}{8}a=3[/tex]
Solution:
First we multiply both sides by 8 to get free of the denominator. That yields [tex]\frac{3}{8}a\cdot8=3\cdot8[/tex], or
3a=24
. Then we divide both sides by 3 to get
a=8
.
Problem 24
Solve the equation
4x - 9 = 2x + 7
.
Solution:
4x-9=2x+7
2x=16
x=16/2
x=8
Problem 25
If [tex]5x+12=3x-24[/tex], determine the value of
x
.
Solution:
[tex]5x-3x=-24-12[/tex]
[tex]2x=-36[/tex]
[tex]x=-18[/tex]
Problem 26
Find the solution to the equation [tex]\frac{x}{5}=8[/tex].
Solution:
We multiply both sides by 5: [tex]5\cdot\frac{x}{5}=8\cdot5[/tex] in order to get
x=40
.
Problem 27
If
28 = 10y - 3y
, find
y
.
Solution:
We substract on the right side:
28=7y
. Then we divide by 7 in order to get the solution,
y=4
.
Problem 28
-2х - 6 = 2
Solution:
-2х = 2 + 6
-2х = 8
х= -8 : 2
х= -4
Problem 29 sent by Bhoomi Bembde
If 19 + 19x = 3x - 9 find the value of x.
Solution:
19 + 19x = 3x - 9
19x - 3x= -9 - 19
+16x = -28
x= -28 ÷ 16
x= -1.75 or -7/4
Problem 30 sent by Oshin Patel
If x + 7 = 16 then what is the value of 8x - 72 = ?
Solution:
x + 7 = 16
x = 16 - 7
x = 9
8x - 72 = 8 × 9 - 72 = 72 - 72=0
Problem 31
3x + 3 = 7x - 9
Solution:
Subtract 3x from both sides of the equation. 3x + 3 - 3x = 7x - 9 - 3x
3 = 4x - 9
Add 9
3 + 9 = 4x - 9 + 9
12 = 4x
Divide by 4
3 = x
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