Question

How do you solve the multi-step equations by combining like terms?

Answer 1

Hint: The multi-step equation can be solved by using 3 steps. In step1, we need to remove the parentheses or brackets if given in the equation. In step2, we move the like terms in the equation to one side and simplify them. In step3, we need to isolate the unknown variable to find the solution for the equation.

Complete step by step solution:
The variable is a quantity whose value keeps changing according to the context of a mathematical problem or experiment.
We generally denote variables using single small letters such as x, y, z.
A constant is a quantity whose values do not change under a given set of conditions or problem statements.
Examples: numbers.
The like terms in algebra mean that the terms have the same variable and same power.
Examples: 5x and 3x are like terms as they have the same variable and power.
Likewise, 3 and 5 are also like terms as they have the same variable and power.
Multi-step equations require more than two operations such as addition, subtraction, multiplication, and division to solve the equation unlike one-step and two-step equations.
The main objective of the multi-step equation is to isolate the unknown variable to one side of the equations and constants to the other side of the equations.
The equation has both variables and constants.
Steps to solve a multi-step equation:
1) Remove the parentheses by using distributive property if given.
2) Move the like terms to one side of the equation and simplify them.
3) Isolate the unknown variable to find the solution of the equation.
The law of equations is very important to solve any linear equation. The law states that whatever you do to one side of the equation, the same should be applied to the other side.
Let us look at a multi-step equation and see how it is solved.
Solve the equation $10x-5x+20=39-9$
Step 1: Remove the brackets or parenthesis.
The given equation $10x-5x+20=39-9$ does not contain any brackets or parenthesis.
Step 2: Move the like terms to one side of the equation and simplify them.
The given equation $10x-5x+20=39-9$ has like terms.
10x and 5x are like terms.
39 and 9 in the equation are also like terms.
Moving the like terms to one side of the equation,
$\Rightarrow 10x-5x+20=39-9$
Simplifying the like terms,
$\Rightarrow 5x+20=30$
Step 3: Isolate the unknown variable to find the solution of the equation.
The value of x should be isolated.
Subtract 20 from both sides of the equation,
$\Rightarrow 5x+20-20=30-20$
$\Rightarrow 5x=10$
Dividing by 5 on both sides of the equation,
$\Rightarrow \dfrac{5x}{5}=\dfrac{10}{5}$
$\Rightarrow x=2$

Note: The unknown variable in the equation can be isolated on any side but it makes more sense to isolate the variable on the left-hand side as the equation is read from left to right. It is very important to follow the law of equations while solving any linear equation. The law states that whatever you do to one side of the equation, the same should be applied to the other side.