Question

Solve the inequalities for real x for the following equation: $\frac{1}{2}( \frac{3x}{5} +4)\geq \frac{1}{3} (x - 6)$.

Answer 1

$\dfrac{1}{2}( \dfrac{3x}{5} +4)\geq \dfrac{1}{3} (x - 6).$

Distribute 1/2 and 1/3:

$\dfrac{3x}{10} + 2 \geq \dfrac{x}{3} - 2$

Subtract x/3 and -2 from both sides:

$\dfrac{3x}{10} - \dfrac{x}{3} \geq - 2 - 2$

Combine like terms:

$-\dfrac{x}{30} \geq - 4$

Multiply both sides by -30

$x \leq 120$