# How do you solve and check your solutions to -4q=52?

Oct 7, 2016

$q = - 13$

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{- 4 q = 52}$

Divide both sides by $\textcolor{b l u e}{4}$

$\textcolor{b r o w n}{- \frac{4}{\textcolor{b l u e}{4}} \times q = \frac{52}{\textcolor{b l u e}{4}}}$

But $- \frac{4}{4} = - 1$

$- 1 \times q = 13$

$- q = 13$

Multiply both sides by $\left(- 1\right)$ giving

$+ q = - 13$

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Check: Substitute $- 13$ for $q$

=>color(brown)(-4q=52)" "->" "color(blue)(-4(-13)=52

Consider the left hand side (LHS) of the equation.

Minus times minus gives plus (positive) and $4$ is the same as $2 \times 2$

so $4 \times 13 \text{ }$ is the same as

$\text{ } 2 \times 2 \times 13 \to 2 \times 26 \to 52 \to L H S$

So LHS=RHS=52