Question

Caleb solved this equation and recorded his work. 7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6 1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6 2. 15.6x − 16.4 = −2.3x + 35.4 3. 17.9x − 16.4 = 35.4 4. 17.9x = 51.8 5. X ≈ 2.89 When Caleb verified his solution, it didn't work. What mistake did he make? In step 1, the distributive property was not used properly on the right side of the equation. In step 2, the like terms were not combined properly on the right side of the equation. In step 3, the addition property of equality was not used properly to isolate the variable term. In step 5, the division property of equality was not used properly to solve for x.

Answer 1

The correct answer is b. In step 2, the like terms were not combined properly on the right side of the equation.

Answer 2

Option B.

Explanation:

The given equations is

`7.4x+4.1(2x-4)=-2.3(x-6)-21.6`

The correct steps to solve the above equation are

1. Using distributive property, we get

`7.4x+8.2x-16.4=-2.3x+13.8-21.6`

2. Combining like terms, we get

`15.6x-16.4=-2.3x-7.8`

3. Using addition property of equality, add 2.3x on both sides.

`17.9x-16.4=-7.8`

4. Using addition property of equality, add 16.4 on both sides.

`17.9x=8.6`

5. Using division property of equality, divide both sides by 17.9.

`x\approx 0.48`

In step 2, the like terms were not combined properly on the right side of the equation.

`13.8-21.6=-7.8\\eq 35.4`

Therefore, the correct option is B.