Question

solve for x and graph the solution on the number line below.

( x - 9 leq -4 )

answer attempt 1 out of 2

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12
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Explanation:

Step1: Add 9 to both sides

To solve for \( x \) in the inequality \( x - 9 \leq -4 \), we add 9 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.

\[
x - 9 + 9 \leq -4 + 9
\]

Step2: Simplify both sides

Simplifying the left side, \( x - 9 + 9 \) simplifies to \( x \). Simplifying the right side, \( -4 + 9 = 5 \). So we get:

\[
x \leq 5
\]

Answer:

Inequality Notation: \( x \leq 5 \)

For the number line: We would draw a closed circle at 5 (since the inequality is "less than or equal to") and shade to the left of 5 to represent all values of \( x \) that are less than or equal to 5.