Question

solve the inequality. graph the solution.

1. $8y - 5 < 3$
2. $3p + 2 \geq -10$
3. $2 > 8 - \frac{4}{3}h$
4. $-2 > \frac{m}{6} - 7$
5. $-1.2b - 5.3 \geq 1.9$
6. $-1.3 \geq 2.9 - 0.6r$

Explanation:

Problem 5: \( 8y - 5 < 3 \)

Step 1: Add 5 to both sides

To isolate the term with \( y \), we add 5 to both sides of the inequality.
\( 8y - 5 + 5 < 3 + 5 \)
\( 8y < 8 \)

Step 2: Divide both sides by 8

To solve for \( y \), we divide both sides by 8.
\( \frac{8y}{8} < \frac{8}{8} \)
\( y < 1 \)

Step 1: Subtract 2 from both sides

To isolate the term with \( p \), we subtract 2 from both sides.
\( 3p + 2 - 2 \geq -10 - 2 \)
\( 3p \geq -12 \)

Step 2: Divide both sides by 3

To solve for \( p \), we divide both sides by 3.
\( \frac{3p}{3} \geq \frac{-12}{3} \)
\( p \geq -4 \)

Step 1: Subtract 8 from both sides

To isolate the term with \( h \), we subtract 8 from both sides.
\( 2 - 8 > 8 - \frac{4}{3}h - 8 \)
\( -6 > -\frac{4}{3}h \)

Step 2: Multiply both sides by \( -\frac{3}{4} \) (and reverse the inequality)

When multiplying or dividing an inequality by a negative number, we reverse the inequality sign.
\( -6 \times (-\frac{3}{4}) < -\frac{4}{3}h \times (-\frac{3}{4}) \)
\( \frac{18}{4} < h \)
Simplify \( \frac{18}{4} \) to \( \frac{9}{2} \) or \( 4.5 \).
\( h > \frac{9}{2} \) (or \( h > 4.5 \))

Answer:

\( y < 1 \)

Problem 6: \( 3p + 2 \geq -10 \)