what is the value of x in the equation \\frac{2}{3}(\\frac{1}{2}x + 12)=\\frac{1}{2}(\\frac{1}{3}x +…
what is the value of x in the equation \\frac{2}{3}(\\frac{1}{2}x + 12)=\\frac{1}{2}(\\frac{1}{3}x + 14)-3?\n-24\n-6\n-\\frac{2}{3}\n0
Answer
Explanation:
Step1: Expand both sides
$$\frac{2}{3}\times\frac{1}{2}x+\frac{2}{3}\times12=\frac{1}{2}\times\frac{1}{3}x+\frac{1}{2}\times14 - 3$$ $$\frac{1}{3}x + 8=\frac{1}{6}x+7 - 3$$
Step2: Simplify the right - hand side
$$\frac{1}{3}x + 8=\frac{1}{6}x + 4$$
Step3: Move terms with (x) to one side
$$\frac{1}{3}x-\frac{1}{6}x=4 - 8$$
Step4: Find a common denominator and calculate
$$\frac{2}{6}x-\frac{1}{6}x=-4$$ $$\frac{1}{6}x=-4$$
Step5: Solve for (x)
$$x=-4\times6=-24$$
Answer:
(-24)