Question

Solve algebraically for x: -2/3(x+12)+2/3x=-5/4x+2 pls explain​

Answer 1

x = 8

Explanation:

Given equation:

`(-2)/(3) (x+12)+(2x)/(3) =(-5x)/(4) +2`

Start out by simplifying the distributive property on the left hand side.

`\implies (-2x)/(3) + ((-24))/(3) +(2x)/(3) =(-5x)/(4) +2`

Combine like terms on the left hand side.

`\implies x\huge\text{(}(-2)/(3) + (2)/(3)\huge\text{)}+ ((-24))/(3) =(-5x)/(4) +2`

Simplify the left hand side.

`\implies x\huge\text{(}0\huge\text{)}+ ((-24))/(3) =(-5x)/(4) +2`

`\implies x\huge\text{(}0\huge\text{)} - 8 =(-5x)/(4) +2`

`\implies0- 8 =(-5x)/(4) +2`

`\implies-8 =(-5x)/(4) +2`

Subtract 2 both sides.

`\implies-8 -2 =(-5x)/(4) +2 - 2`

`\implies-10 =(-5x)/(4)`

Use cross multiplication.

`\implies-10 * 4 =-5x`

`\implies-40 =-5x`

Divide -5 both sides.

`\implies (-40)/(-5) =(-5x)/(-5)`

`\implies 8=x`

Thus, the value of x is 8.

Answer 2

x = 8

Explanation:

Given equation:

`-\frac23(x+12)+\frac23x=-\frac54x+2`

Multiply both sides by 3:

`\implies -2(x+12)+2x=-(15)/(4)x+6`

Multiply both sides by 4:

`\implies -8(x+12)+8x=-15x+24`

Expand brackets:

`\implies -8x-96+8x=-15x+24`

Combine like terms:

`\implies -96=-15x+24`

Add 15x to both sides:

`\implies 15x-96=24`

Add 96 to both sides:

`\implies 15x=120`

Divide both sides by 15:

`\implies x=8`