Question

How do you solve $8\left( x-100 \right)-3=837$ using the distributive property?

Answer 1

Hint: We should always remember that $a\left( b+c \right)=ab+ac.$ From this we will get $a\left( b-c \right)=ab-ac.$ These properties are called the distributive properties. We will apply this property in the given equation. Then, we will transpose the terms accordingly.

Complete step by step solution:
Let us consider the given equation $8\left( x-100 \right)-3=837.$
We are asked to solve the given equation using the distributive property.
We need to multiply the term outside the bracket with the terms inside the bracket. That is what the distributive property says.
Let us first recall what the distributive properties are.
The distributive property is given by $a\left( b+c \right)=ab+ac.$
We have an alternative version of the distributive property that shows that the number can be distributed even if there is minus instead of plus.
That is given by $a\left( b-c \right)=ab-ac.$
Now we are going to apply this property in the given equation to get $8x+8\times 100-3=837.$
In the step, we will multiply and then subtract the constant terms on the left-hand side of the equation accordingly.
We will get $8x-800+3=8x-797=837.$
We will transpose the constant term from the left-hand side of the equation to the right-hand side of the equation.
Then, we will get $8x=837-797=40.$
Let us transpose $8$ from the left-hand side to the right-hand side of the equation to get $x=\dfrac{40}{8}=5.$

Hence the value of $x=5.$

Note: Since $b-c=b+\left( -c \right),$ we do not have to mention the alternative version of the distributive property separately. It is default when we write the real version of the distributive property. Also, we say that the multiplication is distributive over addition and subtraction.