Question

Emily is solving the equation 2(x+9) = 4 (x+7) + 2. Her steps are shown below

Step 1. 2(x+9) = 4(x+7) + 2

Step 2. 2x + 18 = 4x + 7 + 2

Step 3. 2x + 18 =4x + 9

Step 4. -8x = 2x

Step 5. -4 = x




Part A. On which step did Emily make the first error?




Part B. Show the correct steps and solution to Emily's original equation?

Answer 1

(Part A.)

Step 2

(Part B.)

Step 1. 2(x + 9) = 4(x + 7) + 2

Step 2. 2x + 18 = 4x + 28 + 2

Step 3. 2x + 18 = 4x + 30

Step 4. -12 = 2x

Step 5. -6 = x

Explanation:

(Part A.)

Emily incorrectly distributes 4(x + 7). This should be 4x + 28 instead of 4x + 7.

(Part B.)

On Step 2, Emily should have properly distributed 4(x + 7) as 4x + 28. Step 4, -8 is not a coefficient of x.