Question

In need some help. i cant figure this out.

Answer 1

x = 1.28

Explanation:

Given equation:

`3 (1)/(2)x-6=2-2(3)/(4)x`

Add 2³/₄x to both sides of the equation:

`\implies 3 (1)/(2)x+2(3)/(4)x-6=2-2(3)/(4)x+2(3)/(4)x`

`\implies 3 (1)/(2)x+2(3)/(4)x-6=2`

Add 6 to both sides of the equation:

`\implies 3 (1)/(2)x+2(3)/(4)x-6+6=2+6`

`\implies 3 (1)/(2)x+2(3)/(4)x=8`

Rewrite the mixed numbers as improper fractions:

`\implies (3 \cdot 2+1)/(2)x+(2 \cdot 4+3)/(4)x=8`

`\implies (7)/(2)x+(11)/(4)x=8`

Make the denominators of the fractions the same:

`\implies (7 \cdot 2)/(2 \cdot 2)x+(11)/(4)x=8`

`\implies (14)/(4)x+(11)/(4)x=8`

`\textsf{Apply the fraction rule} \quad (a)/(c)+(b)/(c)=(a+b)/(c):`

`\implies (14+11)/(4)x=8`

`\implies (25)/(4)x=8`

Multiply both sides by 4:

`\implies 4 \cdot (25)/(4)x=4 \cdot8`

`\implies 25x=32`

Divide both sides by 25:

`\implies (25x)/(25)=(32)/(25)`

`\implies x=(32)/(25)`

Convert the improper fraction to a mixed number:

`\implies x=1 (7)/(25)`

The value of x as a decimal:

`\implies x=1.28`