Solve the inequality. Then check each number that is a solution

Question

2(2x-9)<9
Question 14 options:
5
3
7
6
4

Question 15 (4 points)

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Solve the inequality. Then check each number that is a solution
-3(2n-11)>n+26
Question 15 options:
2
4
1
0
3

Answer 1

Let's solve each inequality step by step.

Question 14: Solve \( 2(2x - 9) < 9 \)

1. Start by distributing on the left side: \[ 4x - 18 < 9 \]

2. Next, add 18 to both sides: \[ 4x < 27 \]

3. Now, divide by 4: \[ x < \frac{27}{4} \quad \text{or} \quad x < 6.75 \]

Now, we will check each provided option to see which are valid solutions.

• Check 5: \( 5 < 6.75 \) (True)
• Check 3: \( 3 < 6.75 \) (True)
• Check 7: \( 7 < 6.75 \) (False)
• Check 6: \( 6 < 6.75 \) (True)
• Check 4: \( 4 < 6.75 \) (True)

Solutions for Question 14: 5, 3, 6, 4.

Question 15: Solve \(-3(2n - 11) > n + 26\)

1. Start by distributing on the left side: \[ -6n + 33 > n + 26 \]

2. Now, add \( 6n \) to both sides: \[ 33 > 7n + 26 \]

3. Next, subtract 26 from both sides: \[ 7 > 7n \]

4. Finally, divide by 7: \[ 1 > n \quad \text{or} \quad n < 1 \]

Now, we will check each provided option to see which are valid solutions.

• Check 2: \( 2 < 1 \) (False)
• Check 4: \( 4 < 1 \) (False)
• Check 1: \( 1 < 1 \) (False)
• Check 0: \( 0 < 1 \) (True)
• Check 3: \( 3 < 1 \) (False)

Solutions for Question 15: 0.