Question

solve for x and graph the solution on the number line below.
2x + 5 ≥ 11 and 2x + 5 < 29
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Solve the first inequality

Solve \(2x + 5\geq11\).
Subtract 5 from both sides: \(2x\geq11 - 5\), so \(2x\geq6\).
Divide both sides by 2: \(x\geq\frac{6}{2}\), thus \(x\geq3\).

Step2: Solve the second inequality

Solve \(2x + 5\lt29\).
Subtract 5 from both sides: \(2x\lt29 - 5\), so \(2x\lt24\).
Divide both sides by 2: \(x\lt\frac{24}{2}\), thus \(x\lt12\).

Answer:

Inequality Notation: \(3\leq x\lt12\)

For the number - line:

• Place a closed circle at \(x = 3\) (because \(x\) can be equal to 3, due to the \(\geq\) sign in \(x\geq3\)).
• Place an open circle at \(x = 12\) (because \(x\) cannot be equal to 12, due to the \(\lt\) sign in \(x\lt12\)).
• Draw a line segment connecting these two points.