Let's solve each of the equations step by step.
Question 1: \[ 15 + 2X = 21 \]
To isolate \( X \):
- Subtract 15 from both sides: \[ 2X = 21 - 15 \] \[ 2X = 6 \]
- Divide by 2: \[ X = 3 \]
Answer: x = 3
Question 2: \[ x^5 = 20 \]
To solve for \( x \), take the fifth root of both sides: \[ x = 20^{1/5} \] This does not yield a straightforward integer. Let's evaluate the possible responses: The closest integer response is: Answer: 4 (This assumes approximate answers, as \( 20^{1/5} \approx 2.5\))
Question 3: \[ 2X + 5 = 25 \]
To isolate \( X \):
- Subtract 5 from both sides: \[ 2X = 25 - 5 \] \[ 2X = 20 \]
- Divide by 2: \[ X = 10 \]
Answer: x = 10
Question 4: \[ -6X + 4 = 22 \]
To isolate \( X \):
- Subtract 4 from both sides: \[ -6X = 22 - 4 \] \[ -6X = 18 \]
- Divide by -6: \[ X = \frac{18}{-6} \] \[ X = -3 \]
Answer: x = -3
Question 5: \[ 8X - 4 = 6X + 2 \]
To isolate \( X \):
- Subtract \( 6X \) from both sides: \[ 8X - 6X - 4 = 2 \] \[ 2X - 4 = 2 \]
- Add 4 to both sides: \[ 2X = 2 + 4 \] \[ 2X = 6 \]
- Divide by 2: \[ X = 3 \]
Answer: x = 3
Now, summarizing the final answers:
- x = 3
- 4
- x = 10
- x = -3
- x = 3