Answer:
- 2(x + 2) + 2 = 2(x + 3) + 1
- 2x + 3(x + 5) = 5(x – 3)
- 5(x + 4) – x = 4(x + 5) – 1
Step-by-step explanation:
To identify solutions, subtract the right side from both sides and simplify.
1. For 2(x + 2) + 2 = 2(x + 3) + 1
Subtract right side: 2(x + 2) + 2 - (2(x + 3) + 1) = 0
Simplify: 2x + 4 + 2 - 2x - 6 - 1 = 0
Which results in -1 = 0, meaning no solutions.
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2. For 2x + 3(x + 5) = 5(x – 3)
Subtract right side: 2x + 3(x + 5) - 5(x – 3) = 0
Simplify: 2x + 3x + 15 - 5x + 15 = 0
This leads to 30 = 0, no solutions again.
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3. Equation 4(x + 3) = x + 12
Subtract right side: 4(x + 3) - (x + 12) = 0
Simplify: 4x + 12 - x - 12 = 0
Equals 3x = 0, so one solution: x = 0.
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4. Equation 4 – (2x + 5) = (–4x – 2)
Subtract right side: 4 – (2x + 5) - (–4x – 2) = 0
Simplify: 4 - 2x - 5 + 4x + 2 = 0
Gives 2x + 1 = 0, meaning one solution: x = -1/2.
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5. Equation 5(x + 4) – x = 4(x + 5) – 1
Subtract right side: 5(x + 4) – x - (4(x + 5) – 1) = 0
Simplify: 5x + 20 - x - 4x - 20 + 1 = 0
Results in 1 = 0, no solution here.
