Question

solve for ( x ) and graph the solution on the number line below. ( x + 3 leq 7 )
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

Explanation:

Step1: Subtract 3 from both sides

To solve the inequality \( x + 3 \leq 7 \), we subtract 3 from both sides of the inequality. This is based on the property of inequalities that subtracting the same number from both sides does not change the direction of the inequality.
\[
x + 3 - 3 \leq 7 - 3
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( x+3 - 3=x \), and simplifying the right - hand side, \( 7 - 3 = 4 \). So we get:
\[
x\leq4
\]

For graphing on the number line:

• We find the number 4 on the number line.
• Since the inequality is \( x\leq4 \), we use a closed circle at 4 (because 4 is included in the solution set) and draw an arrow to the left (to represent all numbers less than or equal to 4).

Answer:

Inequality Notation: \( x\leq4 \)
Number Line: Draw a closed circle at 4 on the number line and an arrow pointing to the left (towards negative infinity) to represent all real numbers \( x \) such that \( x\leq4 \).