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What are multi-step equations and how can be solved?

multi-step equations

Multi-step equations are equations that are solved in more than two steps. Multi-step equations are just a bit more complicated than one-step or two-step equations, but they can be simplified and solved without any problem. Our goal is to find the unknown number, usually given as X, just like in one-step and two-step equations.
There are no specific instructions that we needo to follow when solving multi-step equations. There are just some rules that we can follow to make the calculation easier.
The general rule for solving multi-step equations is that we should always group variables (unknown numbers like X) on one side of the equation and everything else on the other side. Then we just need to do mathematical operations that are given in the equation and solve it.
The order of operations is the same as described in the lesson about two-step equations. First we need to do addition and subtraction then multiplication and division.

Now, let’s solve some examples and show how the calculation is done.

multi-step equations

Before starting any calculation, we need to get rid of the parentheses if they are given in the equation. The resulting equation is:

\ 15 - 3x - 1 = 4x + 4 + 3x

● The resulting equation can be simplified by calculating the given values on each side of the equation.

\ 14 - 3x = 7x + 4

● Now, we need to group the variables on one side and everything else on the other side of the equation. Note that when we transfer a number or variable from one side of the equation to the other side the number or variable changes its sign.

\ 14 - 3x = 7x + 4 - 3x - 7x =- 14 + 4

● Now we need to calculate and simplify the resulting equation.

\ - 10x =- 10

● The result is a one-step equation that can be solved by dividing both sides by 10.
● The result is \ x = 1.

fractions with multi-step equations

Since we don’t have any parentheses we are going to start with grouping variables on one side and everything else on the other side of the equation.

\frac{1}{3}x + 1 = \frac{1}{9}x - \frac{1}{2}

\frac{1}{3}x - \frac{1}{9}x = - \frac{1}{2} - 1

● Now we are going to simplify the equation by calculating the values on each side.

\frac{(3x - 1x)}{9} = \frac{(-1 + 2)}{2}

\frac{2x}{9} = \frac{1}{2}

● After the previous step the equation is simplified. In this step we are going to multiply both sides by 9 to get rid of the fraction on the left side of the equation.

\ (\frac{2x}{9}) * 9 = \frac{1}{2} * 9

\ 2x = \frac{9}{2}

● Now we are going to multiply both sides by 2 to get rid of the fraction on the right side.

\ 2x * 2 = \frac{9}{2} * 2

\ 4x = 9

● The final form of the equation is a one-step equation. To solve it we just need to divide both sides by 4.
● The result is a fraction, \ x = \frac{9}{4} .

multi-step equations in brackets

Since we have parentheses we need to get rid of them. In this example, we are going to multiply everything in the parentheses by 2.

\ x + 2x + 6 = 36

\ 3x + 6 = 36

Now we have a two-step equation. To solve it we need to subtract 6 from both sides.

\ 3x + 6 - 6 = 36 - 6

\ 3x = 30

In the final step we just need to divide both sides by 3 and get the result.

\ 3x : 3 = 30 : 3

\ x = 10

The result is \ x=10.

 

Multi-step equations worksheets

  Integers (255.4 KiB, 649 hits)

  Decimal numbers (299.9 KiB, 321 hits)

  Fractions (575.6 KiB, 409 hits)

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