Question

item 9
question id: 2036717
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

$$7x - 3>2(2x + 3)+x$$
$$7x - 3>4x+6 + x$$

Step2: Combine like terms

$$7x - 3>5x + 6$$

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

$$7x-5x - 3>5x-5x + 6$$
$$2x-3>6$$

Step4: Add 3 to both sides

$$2x-3 + 3>6 + 3$$
$$2x>9$$

Step5: Divide both sides by 2

$$x>\frac{9}{2}$$

Step6: Graph on the number line

Since \(x>\frac{9}{2}=4.5\), we draw an open circle at \(4.5\) (because \(4.5\) is not included in the solution) and draw an arrow to the right.

Answer:

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