Brief course in solving linear equations that require two or more transformations.

1. 3.3 SOLVING MULTI-STEP
EQUATIONS
OBJECTIVE:
TO USE TWO OR MORE TRANSFORMATIONS TO SOLVE AN
EQUATION.
MR. ANIBAL AGUILAR BARAHONA

2. 3.3 SOLVING MULTI-STEP EQUATIONS
As we explained in past sections, solving a linear equation may require
two or more transformations. Use these guidelines in the process of
solving an equation:
• Simplify one or both sides of the equation (if needed).
• Use the inverse operations to isolate the variable.
The process of solving a linear equation may be presented in 4 general
cases:
CASE 1: Combining Like Terms.
CASE 2: Using the Distributive Property.
CASE 3: Distributing a Negative Sign.
CASE 4: Multiplying by a Reciprocal

3. 3.3 SOLVING MULTI-STEP EQUATIONS
CASE 1: COMBINING LIKE TERMS.
Solve the equation 2푥 − 9푥 + 17 = −4
Solution:
2푥 − 9푥 + 17 = −4 Copy the original equation
−7푥 + 17 = −4 Combine the like terms.
−7푥 + 17 − 17 = −4 − 17 Apply the inverse operation.
−7푥 = −21 Combine like terms.
푥 = 3 Divide by -3 both sides.

4. 3.3 SOLVING MULTI-STEP EQUATIONS
CASE 2: USING THE DISTRIBUTIVE PROPERTY.
Solve the equation: 4푥 + 12 푥 − 3 = 28
Solution:
4푥 + 12 푥 − 3 = 28 Copy the original equation.
4푥 + 12푥 − 36 = 28 Apply the Distributive Property.
16푥 − 36 = 28 Combine like terms.
16푥 − 36 + 36 = 28 + 36 Apply the inverse operation.
16푥 = 64 Combine like terms.
푥 = 4 Divide by 16 both sides.

5. 3.3 SOLVING MULTI-STEP EQUATIONS
CASE 3: DISTRIBUTING A NEGATIVE NUMBER.
Solve the following equation: 10푥 − 6 2푥 + 5 = 20
Solution:
10푥 − 6 2푥 + 5 = 20 Copy the original equation.
10푥 − 12푥 − 30 = 20 Distribute -6 in the expression.
−2푥 − 30 = 20 Combine like terms.
−2푥 − 30 + 30 = 20 + 30 Apply the inverse operation.
−2푥 = 50 Combine like terms.
푥 = −25 Divide by – 2 both sides.

6. 3.3 SOLVING MULTI-STEP EQUATIONS
CASE 4: MULTIPLYING BY A RECIPROCAL.
Solve the equation:
4
3
푥 − 7 = −24
Solution:
4
3
푥 − 7 = −24 Copy the original equation.
3
4
4
3
푥 − 7 = −24
3
4
Multiply both sides by the
reciprocal. .
푥 − 7 = −18 Simplify fractions on both sides.
푥 − 7 + 7 = −18 + 7 Apply the inverse operations.
푥 = −11 Simplify like terms.

7. HOMEWORK:
PGS. 148 – 149
EXERCISES 16 to 40