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Practice
Linear(Simple) Equations
Easy
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Difficult
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
Problem 32 sent by Samarth Shivananda Mathad
The sum of two numbers is 45. One of the numbers exceeds the other by 9. Find the numbers.
19, 28
15, 30
18, 27
17, 28
Solution:
Let the number be x.
Then the other number = x + 9
Sum of two numbers = 45
According to the question, x + (x + 9) = 45
⇒ 2x + 9 = 45
⇒ 2x = 45 - 9 (transposing 9 to the R.H.S changes to -9)
⇒ 2x = 36
⇒ 2x/2 = 36/2 (divide by 2 on both the sides)
⇒ x = 18
Therefore, x + 9 = 18 + 9 = 27
Therefore, the two numbers are 18 and 27.
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