1. Solving equations with Rational Coefficients
mathematical sentence formed by placing an “=“ between two expressions
Remember this???
y – 8 = 12
22 = 14 + z
5 ÷ x = 30
11a = 121

2. Equation
Remember this??? x
+ 7 = 10
Left side
Right side
‘x’ has to be 3 in order to make the equation balanced.
Like a scale, the left side and right side must be the same in order to be balanced!

3. Equation 4 7 x
= 10
Right side
Left side
Like a scale, the left side and right side must be the same in order to be balanced!

4. Objective
SWBAT use multiplicative inverses to solve equations with rational coefficients.
Coefficient is the numerical factor of a term that contains a variable
18x + 4 = 360
¾ x = 18
3.15 = 0.45n

5. Section 5.6, “Using Multiplicative Inverses to Solve Equations”
Multiplicative Inverse Property
To solve an equation that has a fractional coefficient, you can multiply each side of the equation by the fraction’s multiplicative inverse.
MULTIPLICATIVE
INVERSE =
RECIPROCAL

6. MULTIPLICATIVE INVERSE–
the product of a number and its multiplicative inverse is 1.

7. Solve for x. -3 1 Multiply each side of the equation
by the MULTIPLICATIVE INVERSE of 4/7
Multiply -3
Divide (cancel) common factors 1

8. Try It Out!! Solve

9. Solve equations with decimal coefficients
To solve an equation with a decimal coefficient, divide each side of the equation by the coefficient
3.15 = .45n
3.15 = .45n Division property of equality
7 = n Simplify

10. Solving Multi-Step Equations
Remember this???
Solving Multi-Step Equations
How can you get the “unknown” by itself?
Solving Equations with Variables on Both Sides
STEP 1- Use distributive property and combine like terms.
STEP 2- Collect variables on one side of the equation.
STEP 3- “Undo” addition and/or subtraction.
STEP 4- “Undo” multiplication and/or division.
STEP 5- Solve for the variable.
STEP 6- Check your work.

11. Solve for x. -1 1 Subtract 4/5 from each side.
Write fractions using LCD
Multiply each side of the equation
by the MULTIPLICATIVE
INVERSE of -7/15 -1
Multiply
Divide (cancel)
common factors 1

12. Try It Out!! Solve

13. Homework
Text page 249, #12-32 evens