Question

solve and graph the solution of $-\frac{3}{2}x + 5 < -\frac{1}{3}x+3$.

Explanation:

Step1: Move terms with x to one - side

Subtract $-\frac{1}{3}x$ from both sides and subtract 5 from both sides:
$-\frac{2}{3}x+\frac{1}{3}x<3 - 5$

Step2: Combine like - terms

$(-\frac{2}{3}+\frac{1}{3})x<-2$
$-\frac{1}{3}x<-2$

Step3: Solve for x

Multiply both sides by - 3. When multiplying an inequality by a negative number, the direction of the inequality sign changes.
$x > (-2)\times(-3)$
$x>6$

Answer:

The solution of the inequality is $x > 6$. On the number - line, we use an open circle at 6 (since 6 is not included in the solution) and draw an arrow to the right of 6.