Question

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

Answer 1

Answer:

x = 8

Step-by-step explanation:

Given equation:

$\dfrac{-2}{3} (x+12)+\dfrac{2x}{3} =\dfrac{-5x}{4} +2$

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

$\implies \dfrac{-2x}{3} + \dfrac{(-24)}{3} +\dfrac{2x}{3} =\dfrac{-5x}{4} +2$

Combine like terms on the left hand side.

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

Simplify the left hand side.

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

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

$\implies0- 8 =\dfrac{-5x}{4} +2$

$\implies-8 =\dfrac{-5x}{4} +2$

Subtract 2 both sides.

$\implies-8 -2 =\dfrac{-5x}{4} +2 - 2$

$\implies-10 =\dfrac{-5x}{4}$

Use cross multiplication.

$\implies-10 \times 4 =-5x$

$\implies-40 =-5x$

Divide -5 both sides.

$\implies \dfrac{-40}{-5} =\dfrac{-5x}{-5}$

$\implies 8=x$

Thus, the value of x is 8.

Answer 2

Answer:

x = 8

Step-by-step explanation:

Given equation:

$-\dfrac23(x+12)+\dfrac23x=-\dfrac54x+2$

Multiply both sides by 3:

$\implies -2(x+12)+2x=-\dfrac{15}{4}x+6$

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:

$\implies x=8$