Question

3(x-2)/4 is lesser than or equal to 2(4+x)/3​

Answer 1

Solution!!

$\sf \dfrac{3(x-2)}{4}\leq \dfrac{2(4+x)}{3}$

Distrubute 3 through the parentheses.

$\sf \to \dfrac{3x-6}{4}\leq \dfrac{2(4+x)}{3}$

Distribute 2 through the parentheses.

$\sf \to \dfrac{3x-6}{4}\leq \dfrac{8+2x}{3}$

Multiply both the sides of the inequality by 12.

$\sf \to \dfrac{3x-6}{4}\times 12\leq \dfrac{8+2x}{3}\times 12$

$\sf \to 3(3x-6)\leq 4(8+2x)$

Distribute 3 through the parentheses.

$\sf \to 9x-18\leq 4(8+2x)$

Distribute 4 through the parentheses.

$\sf \to 9x-18\leq 32+8x$

Move the variable to the left-hand side and change its sign.

$\sf \to 9x-18-8x\leq 32$

Move the constant to the right-hand side and change its sign.

$\sf \to 9x-8x\leq 32+18$

Subtract the terms.

$\sf \to x\leq 32+18$

Calculate the sum.

$\sf \to x\leq 50$

$\sf \to x\in [-\infty ,50]$