Let’s solve each equation step by step while showing the work:
Question 1
Solve the following equation for x: \[ 4x + 7 = 23 \]
Step 1: Subtract 7 from both sides: \[ 4x + 7 - 7 = 23 - 7 \] \[ 4x = 16 \]
Step 2: Divide by 4: \[ \frac{4x}{4} = \frac{16}{4} \] \[ x = 4 \]
Answer: \( x = 4 \)
Question 2
Solve the following equation for x: \[ -5 = 3m - 14 \]
Step 1: Add 14 to both sides: \[ -5 + 14 = 3m - 14 + 14 \] \[ 9 = 3m \]
Step 2: Divide by 3: \[ \frac{9}{3} = \frac{3m}{3} \] \[ m = 3 \]
Answer: \( m = 3 \)
Question 3
Solve the following equation for x: \[ 7(x - 9) = -21 \]
Step 1: Distribute 7: \[ 7x - 63 = -21 \]
Step 2: Add 63 to both sides: \[ 7x - 63 + 63 = -21 + 63 \] \[ 7x = 42 \]
Step 3: Divide by 7: \[ \frac{7x}{7} = \frac{42}{7} \] \[ x = 6 \]
Answer: \( x = 6 \)
Question 4
Solve the following equation for x: \[ 7x - 5 = 3x + 15 \]
Step 1: Subtract 3x from both sides: \[ 7x - 3x - 5 = 15 \] \[ 4x - 5 = 15 \]
Step 2: Add 5 to both sides: \[ 4x - 5 + 5 = 15 + 5 \] \[ 4x = 20 \]
Step 3: Divide by 4: \[ \frac{4x}{4} = \frac{20}{4} \] \[ x = 5 \]
Answer: \( x = 5 \)
Question 5
Solve the following equation for x: \[ 8x - 8 = -4x + 16 \]
Step 1: Add \( 4x \) to both sides: \[ 8x + 4x - 8 = 16 \] \[ 12x - 8 = 16 \]
Step 2: Add 8 to both sides: \[ 12x - 8 + 8 = 16 + 8 \] \[ 12x = 24 \]
Step 3: Divide by 12: \[ \frac{12x}{12} = \frac{24}{12} \] \[ x = 2 \]
Answer: \( x = 2 \)
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