Question

The steps to solve the equation $12(5+3a)+(4a-6)=58$ are given below. Which of the following steps is incorrect?

$\text{I.}$ Multiply 12 with each term.
$12\times 5+12\times 3a+12\times 4a-12\times 6=58$

$\text{II.}$ Simplify the expression.
$60+36a+4a–6=58$

$\text{III.}$ Combine the like terms.
$60-6+36a+4a=58$

$\text{IV.}$ Solve the equation to get the final expression.
$54+40a=58$


$\text{V.}$ Solve the final expression to find the value of a.
$40a=58-54$
$40a=4$
$a=4÷40=\frac{4}{40}=\frac{1}{10}$

• A. Step II and V are incorrect.
• B. Step III is incorrect.
• C. Step I is incorrect.
• D. Step IV is incorrect.

Answer 1

The correct option is C Step I is incorrect.

Given, $12(5+3a)+(4a-6)$

$\text{I.}$ Multiply 5 and 3a by 12 to open the parentheses.
$12\times 5+12\times 3a+4a-6=58$

$\text{II.}$ Simplify the expression.
$60+36a+4a–6=58$

$\text{III.}$ Combine the like terms.
$60-6+36a+4a=58$

$\text{IV.}$ Solve the equation to get the final expression.
$54+40a=58$

$\text{V.}$ Solve the final expression to find the value of a.
$40a=58-54$
$40a=4$
$a=4÷40=\frac{4}{40}=\frac{1}{10}$

We can see that $\text{step I}$ is incorrect. As per the given expression, $12$ will be multiplied with $5$ and $3a$, not with all terms of the equation.