Solve the equation -4(m + 6) = -8 for m.
Understand the Problem
The question is asking to solve an algebraic equation for the variable 'm'. We need to isolate 'm' by performing inverse operations, following the order of operations in reverse (PEMDAS/BODMAS). This involves distributing, combining like terms (if any), and then using addition/subtraction and multiplication/division to get 'm' by itself on one side of the equation.
Answer
$m = 2$
Answer for screen readers
$m = 2$
Steps to Solve
- Distribute the constant
Distribute the $4$ on the left side of the equation to both terms inside the parenthesis:
$$4(3m + 2) = 32$$ $$12m + 8 = 32$$
- Isolate the term with 'm'
Subtract $8$ from both sides of the equation to isolate the term containing $m$:
$$12m + 8 - 8 = 32 - 8$$ $$12m = 24$$
- Solve for 'm'
Divide both sides of the equation by $12$ to solve for $m$:
$$\frac{12m}{12} = \frac{24}{12}$$ $$m = 2$$
$m = 2$
More Information
The solution to the equation $4(3m + 2) = 32$ is $m = 2$. This means that when $m$ is replaced with $2$ in the original equation, the equation holds true. We can check this: $4(3(2) + 2) = 4(6 + 2) = 4(8) = 32$, which confirms our solution.
Tips
A common mistake is to forget to distribute the $4$ to both terms inside the parentheses. For example, some might incorrectly write $12m + 2 = 32$ instead of $12m + 8 = 32$. Another common mistake is performing the operations in the incorrect order. Remember to isolate the term with the variable before dividing.
AI-generated content may contain errors. Please verify critical information
