Question

Can you plz help me with #10

Answer 1

x = 8

Explanation:

`-(2)/(3)(x+12)+(2)/(3)x=-(5)/(4)x+2\qquad\text{multiply both sides by}\ LDM(3,\ 4)=12\\\\12\!\!\!\!\!\diagup^4\left(-(2)/(3\!\!\!\!\diagup_1)\right)(x+12)+12\!\!\!\!\!\diagup^4\cdot(2)/(3\!\!\!\!\diagup_1)x=12\!\!\!\!\!\diagup^3\cdot\left(-(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`

`-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)}\\\\(-120)/(-15)=(-15x)/(-15)\\\\8=x\to x=8`