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

Answer 1

step 3 is the answer as in this we combined the like terms 2x & 6x and got 8x

Answer 2

Answer:

(C) Step 3

Step-by-step explanation:

Combining like terms means to combine the coefficients of the like terms.

By like terms we mean that the terms which are same.

In the question, we are solving the equation: 2(x − 4) + 6x = 9x − 10

Considering Step 3, we are combining the coefficients of x in the L.H.S

The coefficients of x in L.H.S = 2,6

2x  + 6x = 8x

Hence, by combining these two terms, we get a new term that is 8x.

Hence, combining is taking place in step 3. Therefore, correct option is (C).