Let's solve each equation step by step.
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Equation 1: \( 3x + 12 + x = 48 \)
Combine like terms: \[ 4x + 12 = 48 \]
Subtract 12 from both sides: \[ 4x = 48 - 12 \] \[ 4x = 36 \]
Divide by 4: \[ x = \frac{36}{4} = 9 \]
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Equation 2: \( 3x - 12 = 25 + 2x - 2 \)
Simplify the right side: \[ 3x - 12 = 25 - 2 = 23 + 2x \]
Subtract \(2x\) from both sides: \[ 3x - 2x - 12 = 23 \] \[ x - 12 = 23 \]
Add 12 to both sides: \[ x = 23 + 12 \] \[ x = 35 \]
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Equation 3: \( 3 - 6x + 2 = 29 \)
Combine like terms: \[ 5 - 6x = 29 \]
Subtract 5 from both sides: \[ -6x = 29 - 5 \] \[ -6x = 24 \]
Divide by -6: \[ x = \frac{24}{-6} = -4 \]
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Equation 4: \( x + 1 + 4x = 26 \)
Combine like terms: \[ 5x + 1 = 26 \]
Subtract 1 from both sides: \[ 5x = 26 - 1 \] \[ 5x = 25 \]
Divide by 5: \[ x = \frac{25}{5} = 5 \]
Final Solutions:
- From the first equation: \( x = 9 \)
- From the second equation: \( x = 35 \)
- From the third equation: \( x = -4 \)
- From the fourth equation: \( x = 5 \)