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Linear Equation in One Variable Worksheets with Solutions
Example 1.
Solve the following
(i)3x – 9 = 0
(ii)6x – 2 = 8 + x
(iii)8 –3x = 5 – 4x
Solution:
(i)3x – 9 = 0
Given Equation is 3x – 9 = 0
3x=9
x=3
(ii)6x – 2 = 8 + x
Given equation 6x-2=8+x
Transferring constants to one side and variables to another side we have
6x-x=8+2
5x=10
x=10/5
x=2
(iii)8 –3x = 4x-5
Given Equation 8 –3x = 4x-5
Transferring constants to one side and variables to another side we have
8 –3x = 4x-5
8+5=4x+3x
14=7x
x=14/7
x=2
Example 2.
Solve the linear equation 10(y – 2) – 2(y – 3) – 5(y + 3) = 0
Solution:
Given Linear Equation is 10(y – 2) – 2(y – 3) – 5(y + 3) = 0
Simplifying it further we have
10y-20-2y+6-5y-15=0
3y-29=0
3y=29
y=29/3
Example 3.
Simplify 4x + 2(x+3) = 10 – (2x – 5)
Solution:
Given Linear Equation is 4x + 2(x+3) = 10 – (2x – 5)
Moving Constants to one side and Variables to another side we have
4x+2x+6=10-2x+5
6x+6=15-2x
6x+2x=15-6
8x=9
x=9/8
Example 4.
Solve for m in \(\frac { 3m+8 }{ 2 } \) =4m-6?
Solution:
Given \(\frac { 3m+6 }{ 2 } \) = 4m-6
3m+8=2(4m-6)
3m+8 =8m-12
8+12=8m-3m
20=5m
m=20/5
m=4
Example 5.
Solve \(\frac { 5x }{ 3 } \) = \(\frac { 3x }{ 2 } \)+\(\frac { 1 }{ 4 } \)?
Solution:
Given \(\frac { 5x }{ 3 } \) = \(\frac { 3x }{ 2 } \)+\(\frac { 1 }{ 4 } \)
\(\frac { 5x }{ 3 } \) – \(\frac { 3x }{ 2 } \) = \(\frac { 1 }{ 4 } \)
\(\frac { 10x-9x }{ 6 } \) = \(\frac { 1 }{ 4 } \)
4(10x-9x)=1*6
4x=6
x=\(\frac { 6 }{ 4 } \)
x=\(\frac { 3 }{ 2} \)
Example 6.
Solve the equation 0.18(3x – 4) = 0.2x + 0.8
Solution:
Given equation 0.18(3x – 4) = 0.2x + 0.8
0.54x-0.72=0.2x+0.8
0.54x-0.2x=0.8+0.72
0.34x=1.52
x=\(\frac { 1.52 }{ 0.34} \)
Example 7.
Simplify the Linear Equation and get the Value of the Variable \(\frac { x+3 }{ x-3 } \) = \(\frac { 5 }{ 4 } \)?
Solution:
Given Equation \(\frac { x+3 }{ x-3 } \) = \(\frac { 5 }{ 4 } \)
(x+3)4=5(x-3)
4x+12=5x-15
12+15=5x-4x
27=x
Example 8.
Five added to four times a whole number gives 37. Find the number?
Solution:
Let the whole number be x
As per the given condition 5+4 times whole number = 37
5+4(x)=37
5+4x=37
4x=37-5
4x=32
x=32/4
x=8
Example 9.
One-fourth of a number is 15. What will be 25% of that number?
Solution:
Let the number is x
From the given condition \(\frac { 1 }{ 4 } \)(x)=15
x=15*4
x=60
Since we are asked 25% of the number we have 25%(60)
=\(\frac { 25*60 }{100 } \)
=\(\frac { 1500 }{100 } \)
=15
Example 10.
There are 450 students in a school. If the number of girls is 104 more than the boys, how many boys are there in the school?
Solution:
Let the number of boys = x
Then, number of girls = x + 104
As per the given condition x + (x + 104) =450
2x + 104 = 450
2x = 450 – 104= 346
x = 346/2=173
Hence, the number of boys = 173
And, the number of girls = (x + 104)
= 173 + 104
= 277
Example 11.
The Sum of 2 consecutive numbers is 64. Find the numbers?
Solution:
Let the 2 consecutive numbers be x and x+2
As per the given condition x+x+2=64
2x+2=64
2x=64-2
2x=62
x=62/2
x=31
the Other Consecutive Number is x+2 i.e 33
Example 12.
If a rectangle possesses a width of 4 inches and has a perimeter of 16 inches, then what is the length?
Solution:
We know the Perimeter of a Rectangle Formula is p = 2(l+w)
Substituting the given data in the formula we have 16 =2(l+4)
Simplifying further we have 16=2l+8
16-8=2l
8=2l
l=8/2
l=4
Therefore, length of the rectangle = 4 inches