Question

1. $7(2y - 10) > 14$
2. $-4(2x + 5) + x < -13$
3. $-5(-x - 1) + 4x < 50$
4. $9x + 7 < 10x - 4$
5. $-3x < 33$
6. $5.5y < 44$
7. $-x - 8 > 10$
8. $7l - 3 < 4l + 6$
9. $7 - y < 12$

Explanation:

Let's solve each inequality one by one:

Problem 6: \( 7(2y - 10) > 14 \)

Step 1: Divide both sides by 7

To simplify the inequality, we first divide both sides by 7. This gives us:
\( \frac{7(2y - 10)}{7} > \frac{14}{7} \)
Simplifying both sides, we get:
\( 2y - 10 > 2 \)

Step 2: Add 10 to both sides

Next, we add 10 to both sides to isolate the term with \( y \):
\( 2y - 10 + 10 > 2 + 10 \)
Simplifying, we have:
\( 2y > 12 \)

Step 3: Divide both sides by 2

Finally, we divide both sides by 2 to solve for \( y \):
\( \frac{2y}{2} > \frac{12}{2} \)
Simplifying, we get:
\( y > 6 \)

Step 1: Distribute -4

First, we distribute the -4 across the terms inside the parentheses:
\( -4 \times 2x + (-4) \times 5 + x < -13 \)
Simplifying, we get:
\( -8x - 20 + x < -13 \)

Step 2: Combine like terms

Next, we combine the \( x \)-terms:
\( (-8x + x) - 20 < -13 \)
Simplifying, we have:
\( -7x - 20 < -13 \)

Step 3: Add 20 to both sides

Now, we add 20 to both sides to isolate the term with \( x \):
\( -7x - 20 + 20 < -13 + 20 \)
Simplifying, we get:
\( -7x < 7 \)

Step 4: Divide both sides by -7 (and reverse the inequality)

When dividing by a negative number, we reverse the inequality sign:
\( \frac{-7x}{-7} > \frac{7}{-7} \)
Simplifying, we have:
\( x > -1 \)

Step 1: Distribute -5

First, we distribute the -5 across the terms inside the parentheses:
\( -5 \times (-x) + (-5) \times (-1) + 4x < 50 \)
Simplifying, we get:
\( 5x + 5 + 4x < 50 \)

Step 2: Combine like terms

Next, we combine the \( x \)-terms:
\( (5x + 4x) + 5 < 50 \)
Simplifying, we have:
\( 9x + 5 < 50 \)

Step 3: Subtract 5 from both sides

Now, we subtract 5 from both sides to isolate the term with \( x \):
\( 9x + 5 - 5 < 50 - 5 \)
Simplifying, we get:
\( 9x < 45 \)

Step 4: Divide both sides by 9

Finally, we divide both sides by 9 to solve for \( x \):
\( \frac{9x}{9} < \frac{45}{9} \)
Simplifying, we have:
\( x < 5 \)

Answer:

\( y > 6 \)

Problem 8: \( -4(2x + 5) + x < -13 \)