Fundamentals of Math

Fundamentals of Mathematics

Practice 3.4.1

Directions: Solve for the indicated variable.

1. −8 = −24

2.

= 4

4

3. ℎ − 4 = 3

4. 6 + = 10

5. 6 − 4 = −4

6. 8 + 6 + 3 − 2 = 37

Answer Key on Page 119

Variables on Both Sides of the Equal Sign When variables are on both sides of the equal sign, you will need to move all the variables to one side first by doing the inverse operation before you can begin solving for (or the variable).

Example 3.4.4

9 − 3 = 5 + 6

⟹ 9 − 3 − 5 = 5 − 5 + 6

⟹ 9 − 9 − 8 = 6 − 9 ⟹ −8 = −3

−8

−3 −8

⟹

=

−8

3 8

⟹ =

Cross Multiplication When solving equations that involve fractions that contain a variable (see Example), things can appear tricky. The best thing to do is to simplify the equation before you begin solving for the unknown. When a single fraction equals another single fraction, you can cross multiply . This will eliminate the fractions altogether and then solve the equation as usual.

Example 3.4.5

5 − 2

3 + 4

=

Multiply the numerator (5) of the first fraction by the denominator ( + 4) of the second fraction and set that equal to the product of the denominator of the first fraction ( − 2) and the numerator of the second fraction (3) .

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