Solving Multi-Step Equations Define like terms again: Terms with exactly the same variables....

Solving Multi-Step EquationsSolving Multi-Step Equations

Define like terms again: Terms with exactly the same variables.

Examples:

Define the distributive property again: 6(3x + 2)

Example:

**Steps for Solving a Multi-Step Equation**

Step 1 Clear the equation of fractions and decimals.

Step 2 Use the Distributive Property to remove parentheses on each side.

Step 3 Combine like terms on each side.

Step 4 Undo addition or subtraction.

Step 5 Undo multiplication or division.

Solve 3a + 6 + a = 90

4a + 6 = 90 Combine like terms.

-6 -6 Subtract 6 from each side.

4a = 84 Simplify.

3a + 6 + a = 90Check:

Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3

2-3

= Divide each side by 4.

a = 21 Simplify.

4a4

844

You try:You try:

3x – 4x + 6 = -23x + (-4x) + 6 = -2 - 1 x + 6 = -2 combined like terms

-6 -6 subtract - 1x = -8 get rid of the negative variable

x = 8

7 = 4m – 2m + 1 7 = 4m + (-2m) + 1 7 = 2m + 1-1 -16 = 2m2 2m = 3

Don’t Forget: CHECK your

solution

Solve 2(x – 6) = 8

2x – 12 = 8 Use the Distributive Property.

+12 +12 Add 6 to each side.

2x = 20 Simplify.

x = 10 Simplify.


2-3

= Divide each side by 2. 2x2

202

2x + (-12) = 8

You try:You try:

3 ( k + 8 ) = 21

3k + 24 = 21

- 24 -24

3k = -3

3 3

k = -1

15 = -3(x – 1) + 9

15 = -3x – (-3) + 915 = -3x + 3 + 915 = -3x + 12-12 -123 = -3x-3 -3

-1 = x

You need to build a rectangular pen in your back yard for

your dog. One side of the pen will be against the house. Two sides of

the pen have a length of x ft and the width will be 25 ft. What is the

greatest length the pen can be if you have 63 ft of fencing?

Relate: length plus 25 ft plus length equals amount of side of side of fencing

Define: Let x = length of a side adjacent to the house.

Write: x + 25 + x = 63


2-3

x + 25 + x = 63

The pen can be 19 ft long.

2x + 25 = 63 Combine like terms.

– 25 = – 25 Subtract 25 from each side.

2x = 38 Simplify.

x = 19


2-3

(continued)

= Divide each side by 2. 2x2

382

Solve + = 173x2

x5

15x + 2x = 170 Multiply.

17x = 170 Combine like terms.

x = 10 Simplify.


2-3

Method 2: Multiplying to clear fractions

10( + ) = 10(17) Multiply each side by 10, a commonmultiple of 2 and 5.

3x2

x5

10( ) + 10( ) = 10(17) Use the Distributive Property.3x2

x5

= Divide each side by 17.17x17

17017

You try:You try:

2nd method:

¼ m + ½ m = 5/8

(8) ¼ m + (8) ½ m = 5/8 ( 8)

2m + 4m = 5

6m = 5

6 6

m = 5/6

Solve 0.6a + 18.65 = 22.85.


2-3

Solving Multi-Step Equations Define like terms again: Terms with exactly the same variables....

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