Question

1/4x-2=-6+5/12x solve the equation for the variable​

Answer 1

Answer:

$\huge\boxed{x=24}$

Step-by-step explanation:

$\dfrac{1}{4}x-2=-6+\dfrac{5}{12}x\qquad|\text{add 2 to both sides}\\\\\dfrac{1}{4}x-2+2=-6+2+\dfrac{5}{12}x\\\\\dfrac{1}{4}x=-4+\dfrac{5}{12}x\qquad|\text{subtract}\ \dfrac{5}{12}x\ \text{from both sides}\\\\\dfrac{1}{4}x-\dfrac{5}{12}x=-4+\dfrac{5}{12}x-\dfrac{5}{12}x\\\\\dfrac{1\cdot3}{4\cdot3}x-\dfrac{5}{12}x=-4\\\\\dfrac{3}{12}x-\dfrac{5}{12}x=-4\\\\\dfrac{3-5}{12}x=-4\\\\\dfrac{-2}{12}x=-4\\\\\dfrac{-2:2}{12:2}x=-4$

$-\dfrac{1}{6}x=-4\qquad|\text{multiply both sides by (-6)}\\\\\left(-6\!\!\!\!\diagup\right)\cdot\left(-\dfrac{1}{6\!\!\!\!\diagup}\right)x=(-4)(-6)\\\\x=24$