Question

How do you solve $75=-5\left( 3+6m \right)$ using the distributive property?

Answer 1

Hint: To solve such questions using the distributive property, just simply open the parenthesis and multiply the numbers outside the parentheses to those inside them. After opening the parenthesis, just simplify the expression to get the final answer.

Complete step by step answer:
The Distributive property is one of the most commonly used properties in mathematics which can help in many mathematical problems.
Given:
The equation: $75=-5\left( 3+6m \right)$
In the given expression above, we will use the distributive property while opening the parenthesis. Distributive property states that if an expression $a\left( b+c \right)$is given then, it can also be written as$\Rightarrow a\left( b+c \right)=ab+bc$
Applying the same concept in the given equation we get,
$\Rightarrow 75=-5\times 3+\left( -5 \right)\times 6m$
Now, multiply the terms together to get the following equation,
$\Rightarrow 75=-15-30m$
To further simplify the above expression, transpose the constants on one side of the equation and the variables on the other side of the equation, which will give us,
$\Rightarrow 30m=-15-75$
Simplifying the expression further by adding the negative numbers together, we get,
$\Rightarrow 30m=-90$
Now, divide both the sides of the above equation by$30$, to get the following equation,
$\Rightarrow \dfrac{30m}{30}=\dfrac{-90}{30}$
Cancelling the numerators and denominators on both sides by their common factor, we get
$\Rightarrow m=-3$

Hence, by using the distributive property to solve the given equation$75=-5\left( 3+6m \right)$, we get the value of $m$ as $m=-3$.

Note: Distributive property can be used over many mathematical operations which include, distributive property over addition, distributive property over subtraction, distributive property over fractions, distributive property over exponents, and distributive property over variables.
While solving these kinds of questions while using distributive property it is very important to keep in mind the signs while opening the parenthesis.