Question

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

Explanation:

Step1: Expand the right - hand side

$$\begin{align*} 7x - 3&>2(2x + 3)+x\\ 7x-3&>4x + 6+x \end{align*}$$

Step2: Combine like terms

$$\begin{align*} 7x-3&>5x + 6 \end{align*}$$

Step3: Subtract \(5x\) from both sides

$$\begin{align*} 7x-5x-3&>5x-5x + 6\\ 2x-3&>6 \end{align*}$$

Step4: Add 3 to both sides

$$\begin{align*} 2x-3 + 3&>6+3\\ 2x&>9 \end{align*}$$

Step5: Divide both sides by 2

$$\begin{align*} x&>\frac{9}{2}=4.5 \end{align*}$$

To graph \(x > 4.5\) on the number line:

• Draw an open circle at \(x = 4.5\) (because \(x\) is not equal to \(4.5\)).
• Draw an arrow to the right of \(4.5\) (since \(x\) is greater than \(4.5\)).

Answer:

The solution of the inequality \(7x - 3>2(2x + 3)+x\) is \(x>\frac{9}{2}\) or \(x > 4.5\). On the number - line, we use an open circle at \(4.5\) and an arrow pointing to the right.