Question

How do you solve the multi steps equation with distributive property?

Answer 1

Hint: We know that the distributive property is the method for removing parentheses. So, first introduce the simplification and the elimination steps of both the constants and the variable and then divide the remaining by coefficient of variable to get the answer.

Complete step by step answer:
Let us first understand the method of solving the multi – steps equation with distributive property step by step and then we will look at an example for the same.
Step 1:
Simplify both the sides of the equation using the distributive property.
Step 2:
Now, eliminate all the constant terms from the left hand side.
Step 3:
Now, eliminate all the variable terms from the right hand side.
Step 4:
Now, if the variable in the left hand side, if it has any coefficient, divide the whole equation by that.

Additional information:
Now, let us understand the same using the example of solving: $4 (x + 1) = 9 + x$
Step 1:
As mentioned in step 1, we will first simplify each of the sides. Since, we can clearly see that the right hand side is already very simplified, so, we will work on the left hand side only. We will then obtain: $4x + 4 = 9 + x$
Step 2:
Now, we need to eliminate the constant terms from the left hand side. As we see there are 4 on the left hand side. We will take it from addition in the left hand side to subtraction in the right hand side. We will then obtain: $4x = 9 – 4 + x$
Simplifying it further, we will get: $4x = 5 + x$
Step 3:
Now, we need to eliminate the variable terms from the right hand side. As we see there is x on the right hand side. We will take it from addition in the right hand side to subtraction in the left hand side. We will then obtain: $4x – x = 5$
Simplifying it further, we will get: $3x = 5$
Step 4:
Now, we will divide the whole equation by 3 because the coefficient of $x$ is 3. We will then obtain: $x = \dfrac{5}{3}$

Note: Distributive property is given by the following expression: $a (b + c) = ab + ac$. In the example above, we just took a = 4, b = x and c = 1.
Basically taking all the variables on one side and constants on the other so that we get a clear and simple equation.