Question

consider the sequence of steps to solve the equation: 2(x - 4) + 6x = 9x - 10
given ⇒ 2(x - 4) + 6x = 9x - 10
step 1 ⇒ 2x - 8 + 6x = 9x - 10
step 2 ⇒ 2x + 6x - 8 = 9x - 10
step 3 ⇒ 8x - 8 = 9x - 10
step 4 ⇒ 8x - 8x - 8 = 9x - 8x - 10
step 5 ⇒ 0 - 8 = x - 10
step 6 ⇒ -8 = x - 10
step 7 ⇒ -8 + 10 = x - 10 + 10
step 8 ⇒ 2 = x + 0
step 9 ⇒ 2 = x
which step in solving this equation is justified by combining like terms?
a step 1 ⇒ 2x - 8 + 6x = 9x - 10
b step 2 ⇒ 2x + 6x - 8 = 9x - 10
c step 3 ⇒ 8x - 8 = 9x - 10
d step 4 ⇒ 8x - 8x - 8 = 9x - 8x - 10

Explanation:

Step1: Define like - terms

Like terms have the same variable(s) raised to the same power(s).

Step2: Analyze Step 1

Step 1 uses the distributive property, not combining like - terms.

Step3: Analyze Step 2

Step 2 is just re - arranging terms, not combining like - terms.

Step4: Analyze Step 3

In Step 3, \(2x+6x\) are combined to get \(8x\) since \(2x\) and \(6x\) are like terms (both have the variable \(x\) to the first power). This step is justified by combining like terms.

Step5: Analyze Step 4

Step 4 is subtracting \(8x\) from both sides of the equation, not combining like terms.

Answer:

C. Step 3 ⇒ 8x - 8 = 9x - 10