Question

solve the inequality and graph it
2x - 3 ≥ -x + 0

Explanation:

Step1: Add \(x\) to both sides

To isolate \(x\) terms, add \(x\) to each side of the inequality \(2x - 3 \geq -x + 0\). This gives \(2x + x - 3 \geq -x + x + 0\), which simplifies to \(3x - 3 \geq 0\).

Step2: Add 3 to both sides

Now, add 3 to both sides to isolate the term with \(x\). So, \(3x - 3 + 3 \geq 0 + 3\), resulting in \(3x \geq 3\).

Step3: Divide by 3

Divide both sides of the inequality \(3x \geq 3\) by 3. Since 3 is positive, the inequality sign remains the same. We get \(\frac{3x}{3} \geq \frac{3}{3}\), which simplifies to \(x \geq 1\).

Answer:

The solution to the inequality \(2x - 3 \geq -x + 0\) is \(x \geq 1\). For the graph, there would be a closed circle at \(x = 1\) (because the inequality is "greater than or equal to") and an arrow pointing to the right (indicating all values greater than or equal to 1).