Question

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

Explanation:

Step1: Move x - terms to one side

Add $\frac{2}{3}x$ to both sides:
$5<-\frac{1}{3}x+\frac{2}{3}x + 3$.

Step2: Simplify x - terms

$5 < \frac{-1 + 2}{3}x+3$, so $5<\frac{1}{3}x + 3$.

Step3: Move constant terms

Subtract 3 from both sides: $5 - 3<\frac{1}{3}x$, which gives $2<\frac{1}{3}x$.

Step4: Solve for x

Multiply both sides by 3: $x>6$.

Answer:

The solution is $x > 6$. On the number - line, you would have an open circle at 6 and an arrow pointing to the right.