Question

9 solve the inequality and represent its solution graphically. 2 + 3x > x - 4

Explanation:

Step1: Move terms with \(x\) to one side

Subtract \(x\) from both sides: \(2 + 3x-x>x - 4-x\), which simplifies to \(2+2x>-4\).

Step2: Isolate the term with \(x\)

Subtract \(2\) from both sides: \(2x+2 - 2>-4 - 2\), so \(2x>-6\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(\frac{2x}{2}>\frac{-6}{2}\), resulting in \(x > - 3\).

Graphically, on the number - line:

• Draw an open circle at \(x=-3\) (because the inequality is \(>\), not \(\geq\)).
• Shade the region to the right of \(x =-3\) (since \(x\) values greater than \(-3\) satisfy the inequality).

Answer:

The solution of the inequality \(2 + 3x>x - 4\) is \(x>-3\). Graphically, it is represented by an open circle at \(x =-3\) and shading to the right of \(x=-3\) on the number - line.