# 1. What is the value of m in the equation 5m – 7 = 6m + 11? (4 points) 18 1 –18 –1 2. Which of these is a simplified form of the equation 7x + 4 = 5 + 3x + 1x? (4 points) 3x = 9 3x = 1 11x = 9 11x = 1 3. What is the value of p in the equation 4p + 3(p + 4) = 12p + 12? (4 points) 12 1 0 –1 4. How many solutions can be found for the equation 5x + 3(x – 1) = 10x – 2x – 3? (4 points) None One Two Infinitely many 5. The work of a student trying to solve the equation 3(4x – 2) = 9 + 2x + 5 is shown below: Step 1: 3(4x – 2) = 9 + 2x + 5 Step 2: 12x – 2 = 14 + 2x Step 3: 12x – 2x = 14 + 2 Step 4: 10x = 16 Step 5: x = 1.6 In which step did the student first make an error and what is the correct step? (4 points) Step 2: 12x – 2 = 4 + 2x Step 2: 12x – 6 = 14 + 2x Step 3: 12x + 2x = 14 + 2 Step 3: 12x – 2x = 14 – 2

1. 5m - 7 = 6m + 11 -7 - 11 = 6m - 5m -18 = m <== 2. 7x + 4 = 5 + 3x + 1x 7x + 4 = 5 + 4x 7x - 4x = 5 - 4 3x = 1 <== 3. 4p + 3(p + 4) = 12p + 12 4p + 3p + 12 = 12p + 12 7p + 12 = 12p + 12 7p - 12p = 12 - 12 -5p = 0 p = 0/-5 p = 0 <=== 4. 5x + 3(x - 1) = 10x - 2x - 3 5x + 3x - 3 = 8x - 3 8x - 3 = 8x - 3 infinite solutions <== 5. 3(4x - 2) = 9 + 2x + 5 mistake was made in step 2 ..did not distribute correctly should be : 12x - 6 = 14 + 2x

Question 1: 5m – 7 = 6m + 11 5m - 6m = 11 + 7 -1m = 18 m = -18 Hence, the answer is C. Question 2: 7x + 4 = 5 + 3x + 1x 7x - 1x -3x = 5 - 4 3x = 1 x = [latex] \frac{1}{3} [/latex] Hence, the answer is B. Question 3: 4p + 3(p + 4) = 12p + 12 4p + 3p + 12 = 12p + 12 7p - 12p = 12 - 12 -5p = 0 p = [latex] \frac{0}{-5} [/latex] p = 0 Hence, the answer is C. Question 4: 5x + 3(x – 1) = 10x – 2x – 3 5x + 3x - 3 = 8x - 3 8x - 8x -3 = -3 -3 = -3 Hence, the answer is A. Question 5: 3(4x – 2) = 9 + 2x + 5 12x - 6 = 14 + 2x 12x - 2x = 14 + 6 10x = 20 x = [latex] \frac{20}{10} [/latex] x = 2 Hence, the answer is B.