Question

1. solve each inequality. then graph the solution.

a. $x + 5 > 3$

-4 -2 0 2 4

b. $3 \geq x + 5$

-4 -2 0 2 4

c. $x - \frac{3}{2} < -3$

-6 -5 -4 -3 -2 -1 0

1. elanor is driving below the

speed limit on a highway.

a. write the inequality to
show how much faster
elanor can drive
without going over
the speed limit.

b. solve the inequality you wrote. by how much
can elanor increase her speed?

Explanation:

Problem 4a: Solve \( x + 5 > 3 \)

Step 1: Subtract 5 from both sides

To isolate \( x \), we subtract 5 from both sides of the inequality.
\( x + 5 - 5 > 3 - 5 \)

Step 2: Simplify both sides

Simplifying the left side gives \( x \), and simplifying the right side gives \( -2 \).
\( x > -2 \)

Step 1: Subtract 5 from both sides

Subtract 5 from both sides to isolate \( x \).
\( 3 - 5 \geq x + 5 - 5 \)

Step 2: Simplify both sides

Simplifying the left side gives \( -2 \), and the right side gives \( x \). Rearranging, we get \( x \leq -2 \).
\( -2 \geq x \) or \( x \leq -2 \)

Step 1: Add \( \frac{3}{2} \) to both sides

Add \( \frac{3}{2} \) to both sides to isolate \( x \).
\( x - \frac{3}{2} + \frac{3}{2} < -3 + \frac{3}{2} \)

Step 2: Simplify both sides

Simplify the left side to \( x \). For the right side, convert \( -3 \) to \( -\frac{6}{2} \), then add \( \frac{3}{2} \): \( -\frac{6}{2} + \frac{3}{2} = -\frac{3}{2} \).
\( x < -\frac{3}{2} \) (or \( x < -1.5 \))

Answer:

\( x > -2 \) (Graph: Open circle at -2, arrow to the right)

Problem 4b: Solve \( 3 \geq x + 5 \)