Introduction to math multi steps equations:

An Equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that to be equal on opposite sides of an equal sign. (Source: Wikipedia).

The following rules are used to simplify the equation and the equation does not change.

1) Add or subtract any variable or number to the both sides of the equation

2) Multiply or divide any variable or number to the both sides of the equation.

3) Distributive law also used to eliminate the parentheses in the given equation. Distributive law is a(b + c) = a b + a c.

More than two steps are used to solve the equation is called as multistep equation. Now, we are going to see some of the problems on math multistep equations.

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Problems on math multistep equations:


Example problem 1:

Solve for the variable x: -6 = -4 (9 x + 6)

Solution:

-6 = -4 (9 x + 6)

Use the distributive law, to eliminate the parentheses

-6 = -4 (9 x) - 4 (6)

-6 = -36 x – 24

Add 24 on both sides of the equation

-6 + 24 = -36 x – 24 + 24

18 = - 36 x

Divide by -36 on both sides of the equation

(18 / -36) = -36 x / -36

-1 / 2 = x

So, the answer is x = -1 / 2.

Example problem 2:

Solve for the variable m: m + 10 = -5m + 34

Solution:

m + 10 = -5m + 34

Subtract 10 on both sides of the equation

m + 10 – 10 = -5m + 34 – 10

m = -5m + 24

Add 5m on both sides of the equation

m + 5m = -5m + 5m + 24

6m = 24

Divide by 6 on both sides of the equation

6m / 6 = 24 / 6

m = 4

So, the answer is m = 4.


Few more math multi step equations problems:


Example problem 3:

Solve for the variable x: 7(4t -3) – 1 = 13 + 21t

Solution:

7(4t -3) – 1 = 13 + 21t

To eliminate the parentheses, use the distributive law a (b + c) = a b + a c.

28t – 21 – 1 = 13 + 21t

28t – 22 = 13 + 21t

Add 22 on both sides of the equation

28t – 22 + 22 = 13 + 21t + 22

28t = 21t + 35

Subtract 21t on both sides of the equation

28t – 21t = 21t + 35 – 21t

7t = 35

Divide by 7 on both sides of the equation

7t / 7 = 35 / 7

t = 5

So, the answer is t = 5.

Example problem 4:

Solve the multi step equation for x: - (17 + x) – 6(-2 – x) = 35

Solution:

- (17 + x) – 6(-2 – x) = 35

To eliminate the parentheses, use the distributive law a(b + c) = a b + a c.

-17 – x + 12 + 6x = 35

-1x + 6x – 17 + 12 = 35

5x - 5 =35

Add 5 on both sides of the equation

5x - 5 =35

5x – 5 + 5 = 35 + 5

5x = 40

Divide by 5 on both sides of the equation

5x / 5 = 40 / 5

x = 8

So, the solution is x = 8.

Practice problems on multistep equations:


1)    Solve for the variable t: -1t + 25 = t + 45

(Answer: t = -10)

2)    Solve for the variable y: 3(y + 1) = 7 + y - 13

(Answer: y = -4.5)