Question

solve each inequality and graph its solution.

1. 3 + 2x ≥ 3

Explanation:

Step1: Isolate the variable term

Subtract 3 from both sides of the inequality $3 + 2x\geq3$. We get $3+2x - 3\geq3 - 3$, which simplifies to $2x\geq0$.

Step2: Solve for x

Divide both sides of the inequality $2x\geq0$ by 2. Since 2 is positive, the direction of the inequality sign remains the same. So, $\frac{2x}{2}\geq\frac{0}{2}$, which gives $x\geq0$.

Step3: Graph the solution

On the number - line, we draw a closed circle at 0 (because the inequality is $\geq$, so 0 is included in the solution set) and draw an arrow to the right to represent all the numbers greater than or equal to 0.

Answer:

The solution of the inequality is $x\geq0$. On the number - line, a closed circle is placed at 0 and an arrow extends to the right.