Question

What is the solution of ?
`(5)/(2) x-7=(3)/(4) x+14`

Answer 1

Combine the terms by multiplying into a single fraction.

`\bf{(5)/(2)x-7=(3)/(4)x+14 }`

Find the common denominator.

`\bf{(5x)/(2)-7=(3)/(4)x+14 }`

Combine fractions with the lowest common denominator.

`\bf{(5x(-7))/(2)=(3)/(4)x+14 }`

Multiply the numbers.

`\bf{(5x-14)/(2)=(3)/(4)x+14 }`

Combine the multiplied terms into a single fraction

`\bf{(5x-14)/(2)=(3x)/(4)+14 }`

Find the common denominator.

`\bf{(5x-14)/(2)=(3x)/(4)+(4\cdot14)/(4) }`

Combine fractions with the lowest common denominator.

`\bf{(5x-14)/(2)=(3x+4\cdot14)/(4) }`

Multiply the numbers.

`\bf{(5x-14)/(2)=(3x+56)/(4) }`

Eliminate the denominators of the fractions.

`\bf{4\cdot(5x-14)/(2)=4\cdot(3x+56)/(4) }`

Cancel the multiplied terms that are in the denominator.

`\bf{2(5x-14)=3x+56}`

To distribute.

`\bf{10x-28=3x+56 }`

Add 28 to both sides.

`\bf{10x-28+28=3x+56+28 }`

Simplify

`\bf{10x=3x+84 }`

Subtract 3x from both sides.

`\bf{10x-3x=3x+84-3x }`

Simplify

`\bf{7x=84 }`

Divide both sides by the same factor.

`\bf{x=(84)/(7) }`

Simplify

`\bf{x=12 \ \ \ === > \ \ \ Answer}`

↓

Verification

Let x=12.

1. 
   `\bf{(5)/(2)*12-7=(3)/(4)*12+14 }`
2. 
   `\bf{(5*12)/(2)-7=(3)/(4)*12+14 }`
3. 
   `\bf{(60)/(2)-7=(3)/(4)*12+14 }`
4. 
   `\bf{30-7=(3)/(4)*12+14 }`
5. 
   `\bf{30-7=(3*12)/(4)+14 }`
6. 
   `\bf{30-7=(36)/(4)+14 }`
7. 
   `\bf{30-7=9+14 }`
8. 
   `\bf{23=9+14 }`
9. 
   `\bf{23=23}`

Checked ✅