Question

do you know how?

1. solve each inequality. then graph the solution.

a. ( x + 5 > 3 )
b. ( x + 5 leq 3 )
(there is a number line with marks at -4, -2, 0, 2, 4)

Explanation:

Part a: Solve \( x + 5 > 3 \) and graph the solution

Step 1: Isolate \( x \)

Subtract 5 from both sides of the inequality \( x + 5 > 3 \).
\( x + 5 - 5 > 3 - 5 \)

Step 2: Simplify both sides

Simplify the left - hand side and the right - hand side. The left - hand side \( x+5 - 5=x\), and the right - hand side \( 3 - 5=-2\). So we get \( x > - 2 \).

To graph the solution:

• Draw a number line.
• Locate the point \(-2\) on the number line. Since the inequality is \( x > - 2 \) (not \( x\geq - 2\)), we use an open circle at \(-2\) to indicate that \(-2\) is not included in the solution set.
• Then, draw an arrow to the right of \(-2\) to show that all numbers greater than \(-2\) are part of the solution.

Part b: Solve \( x + 5\leq3 \) and graph the solution

Step 1: Isolate \( x \)

Subtract 5 from both sides of the inequality \( x + 5\leq3 \).
\( x + 5 - 5\leq3 - 5 \)

Step 2: Simplify both sides

Simplify the left - hand side and the right - hand side. The left - hand side \( x + 5-5=x\), and the right - hand side \( 3 - 5=-2\). So we get \( x\leq - 2 \).

To graph the solution:

• Draw a number line.
• Locate the point \(-2\) on the number line. Since the inequality is \( x\leq - 2\), we use a closed circle at \(-2\) to indicate that \(-2\) is included in the solution set.
• Then, draw an arrow to the left of \(-2\) to show that all numbers less than or equal to \(-2\) are part of the solution.

Answer:

a. The solution of \( x + 5>3 \) is \( x > - 2 \).
b. The solution of \( x + 5\leq3 \) is \( x\leq - 2 \).