Answer:
x = 8
Step-by-step explanation:
[tex]-\dfrac{2}{3}(x+12)+\dfrac{2}{3}x=-\dfrac{5}{4}x+2\qquad\text{multiply both sides by}\ LDM(3,\ 4)=12\\\\12\!\!\!\!\!\diagup^4\left(-\dfrac{2}{3\!\!\!\!\diagup_1}\right)(x+12)+12\!\!\!\!\!\diagup^4\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x=12\!\!\!\!\!\diagup^3\cdot\left(-\dfrac{5}{4\!\!\!\!\diagup_1}x\right)+(12)(2)\\\\(4)(-2)(x+12)+(4)(2)x=(3)(-5x)+24\\\\(-8)(x+12)+8x=-15x+24\qquad\text{use the distributive property}\\\\(-8)(x)+(-8)(12)+8x=-15x+24[/tex]
[tex]-8x-96+8x=-15x+24\qquad\text{cancel}\ 8x\ \text{on the left side}\\\\-96=-15x+24\qquad\text{subtract 24 from both sides}\\\\-96-24=-15x+24-24\\\\-120=-15x\qquad\text{divide both sides by (-15)}\\\\\dfrac{-120}{-15}=\dfrac{-15x}{-15}\\\\8=x\to x=8[/tex]
