Question

solve the inequality. graph the solution, if possible.

1. $9x - 6 > 66$
2. $\frac{d}{3}+7 \leq -11$
3. $14.9 - 5.2n < 20.1$
4. $\frac{9}{10} \geq 5z + \frac{3}{10}$
5. $8(p + 3) > 2(4p - 1)$
6. $-\frac{1}{2}(y + 8) < -\frac{1}{4}(2y + 20)$
7. in the united states music industry, an album is awarded gold certification with at least 500,000 albums sold. a recording artist is selling about 1200 albums each day. the artist has already sold 15,000 albums. about how many more days will it take before the album is awarded gold certification?

Explanation:

Problem 1: \( 9x - 6 > 66 \)

Step 1: Add 6 to both sides

To isolate the term with \( x \), we add 6 to both sides of the inequality.
\( 9x - 6 + 6 > 66 + 6 \)
Simplifying, we get \( 9x > 72 \).

Step 2: Divide by 9

To solve for \( x \), divide both sides by 9.
\( \frac{9x}{9} > \frac{72}{9} \)
Simplifying, we find \( x > 8 \).

Step 1: Subtract 7 from both sides

To isolate the term with \( d \), subtract 7 from both sides.
\( \frac{d}{3} + 7 - 7 \leq -11 - 7 \)
Simplifying, we get \( \frac{d}{3} \leq -18 \).

Step 2: Multiply by 3

To solve for \( d \), multiply both sides by 3.
\( \frac{d}{3} \times 3 \leq -18 \times 3 \)
Simplifying, we find \( d \leq -54 \).

Step 1: Subtract 14.9 from both sides

To isolate the term with \( n \), subtract 14.9 from both sides.
\( 14.9 - 5.2n - 14.9 < 20.1 - 14.9 \)
Simplifying, we get \( -5.2n < 5.2 \).

Step 2: Divide by -5.2 (reverse inequality)

When dividing by a negative number, reverse the inequality sign.
\( \frac{-5.2n}{-5.2} > \frac{5.2}{-5.2} \)
Simplifying, we find \( n > -1 \).

Answer:

\( x > 8 \)

Problem 2: \( \frac{d}{3} + 7 \leq -11 \)