Question

an inequality is shown. solve the inequality and graph the solution on the number line. 7x - 3 > 2(2x + 3)+x

Explanation:

Step1: Expand the right - hand side

Expand \(2(2x + 3)+x\):
\[

$$\begin{align*} 2(2x + 3)+x&=4x+6 + x\\ &=5x+6 \end{align*}$$

\]
The original inequality \(7x−3>2(2x + 3)+x\) becomes \(7x−3>5x + 6\).

Step2: Move the \(x\) terms to one side

Subtract \(5x\) from both sides:
\(7x-5x−3>5x-5x + 6\), which simplifies to \(2x−3>6\).

Step3: Isolate the \(x\) term

Add 3 to both sides: \(2x-3 + 3>6+3\), so \(2x>9\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x>\frac{9}{2}=4.5\).

Answer:

The solution of the inequality is \(x > 4.5\). On the number - line, we use an open circle at \(x = 4.5\) (because \(x\) is strictly greater than 4.5) and draw an arrow to the right.