Solving Equations

Using Multiplication and Division

After studying this lesson, you will be able to:

• Solve equations using multiplication and division.

Review of Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by undoing the operation

4. Check by substituting the solution into the original equation

Example 1

	This equation can be solved by cross multiplying.
12r = 120	Use cross multiplication to create a new equation. (5 times r and 12 times 24)
	To isolate the variable we have to undo the 12 times r. The opposite of multiplication is division, so we divide each side by 12.we use the fraction bar symbol for division.
r = 10	12r divided by 12 is r and 120 divided by 12 is 10

Check:

substitute 10 for r in the equation we created by cross multiplying

12 (10) = 120

120 = 120 (always be sure the 2 sides are equal)

Example 2

	First, lets convert the mixed numbers to improper fractions
	Since we have multiplied by m, we need to undo by dividing Remember, dividing by a fraction is done by multiplying by the reciprocal
	Multiply each side by
	cancel out; cross cancel 28 and 7 and 9 and 3 to get

Check:

Substitute for m in the equation where we converted to improper fractions

Example 3

-6x = 11	Since is multiplied by x, we need to undo the operation by dividing by - 6
	Both sides are divided by -6
	In Algebra, we usually leave answers as improper fractions (reduced)

Check by substituting in the original equation

(the s cancel)

11 = 11