Question

solve for x and graph the solution on the number line below. x + 4 ≥ 8. inequality notation: blank. number line: number line with -12 to 12.

Explanation:

Step1: Isolate the variable \( x \)

To solve the inequality \( x + 4 \geq 8 \), we subtract 4 from both sides of the inequality. This is based on the subtraction property of inequalities, which states that if we subtract the same number from both sides of an inequality, the inequality sign remains the same.

$$ x + 4 - 4 \geq 8 - 4 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( x+4 - 4=x \). Simplifying the right - hand side, \( 8 - 4 = 4 \). So we get \( x\geq4 \).

Answer:

The inequality notation is \( x\geq4 \). For the number line, we would draw a closed circle at 4 (since the inequality is "greater than or equal to") and shade the line to the right of 4.