Question

6 graph the solution to the following inequality: -3(x - 3) ≥ -3 + 3x

Explanation:

Step1: Expand the left - hand side

$-3(x - 3)=-3x+9$, so the inequality becomes $-3x + 9\geq-3 + 3x$.

Step2: Move terms with $x$ to one side

Add $3x$ to both sides: $-3x+3x + 9\geq-3 + 3x+3x$, which simplifies to $9\geq-3 + 6x$.

Step3: Isolate the term with $x$

Add 3 to both sides: $9 + 3\geq-3+3 + 6x$, getting $12\geq6x$.

Step4: Solve for $x$

Divide both sides by 6: $\frac{12}{6}\geq\frac{6x}{6}$, so $x\leq2$.

Answer:

The solution set is all real numbers $x$ such that $x\leq2$. On a number - line, you would draw a closed circle at 2 (because the inequality is $\geq$) and shade to the left of 2.