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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