Objectives: • Solve Two-Step linear equations

• Model the steps for solving linear equations

• Write an equation that symbolically expresses a problem solving situation.

Section 2-2 Solve two-step Equations

SPI 11B: identify the opposite of a rational numberSPI 21E: Solve one and two step linear equations

Solve a Two-step Linear Equation

3x - 2 = 4

1. Circle all terms with a variable: 3x - 2 = 4

2. Do all addition and subtraction first: 3x - 2 = 4 +2 +2 Add 2 to both sides 3x = 6 Simplify

3. Write your new equation. 3x = 6

4. Solve using Multiplication or Division. 3x = 6 3 3 Divide each side by 3 x = 2 Simplify

Solve 13 = + 5.y3

24 = y Simplify.

13 – 5 = + 5 – 5 Subtract 5 from each side.y3

8 = Simplify. Write your new equation.y3

3 • 8 = 3 • Multiply each side by 3.y3

Check: 13 = + 5y3

13 + 5 Substitute 24 for y.243

13 8 + 5

13 = 13

Add or subtract first then multiply or divide

Practice: Solve a two-step Linear Equation

Circle the term with the variable and then leave it alone until the end.

Solve 21 = –p + 8

21 – 8 = –p + 8 – 8 Subtract 8 from each side.

13 = –p Simplify. Write your new equation

13 = - p Use the Division Property -1 -1 of Equality. Divide each side

by –1.

–13 = p Simplify.

Check: 21 = –p + 8

21 –(–13) + 8 Substitute –13 for p.

21 = 21 Simplify.

Solve by multiplying by -1

Practice: Solve a two-step Linear Equation

Circle the term with the variable and then leave it alone until the end.

Solve the equation s = d for d.

t

Physical Science Meets Algebra

Circle the term you want to solve for.

s = d

tUse the multiplication property of equality to solve for d.

t ∙ s = d ∙ t t

t ∙ s = d ∙ t t

Simplify the equation.

Rewrite the equation.ts = d

How does the equation relate to physical science?

Solve 8 = – + 4. Justify each step.

–96 = c Simplify.

c24

8 – 4 = – + 4 – 4 Subtraction Property of Equalityc

24

4 = – Simplify.c

24

–24(4) = (–24)(– ) Multiplication Propertyof Equality

c24

3 – 5z – 3 = 18 – 3 Subtraction Property of Equality

–5z = 15 Simplify.

z = –3 Simplify.

Solve 3 – 5z = 18. Justify each step.

Check: 3 – 5(-3) = 18

3 + 15 = 18

Geometry Meets Algebra

In the triangle, the measure of = the measure of Find the value of x.

A B

Step 1: Write an equation to show the relationship between the two angles.

4x + 1 = 63

Step 2: Solve the equation for x. 4x + 1 = 63 original equation4x + 1 – 1 = 63 – 1 SPE 4x = 62 Simplify x = 15.5 DPE

You order iris bulbs from a book. Iris bulbs cost $.90 each. The shipping

charge is $2.50. If you have $18.50 to spend, how many iris bulbs can

you order?

0.90b + 2.50 = 18.50

0.90b + 2.50 – 2.50 = 18.50 – 2.50

0.90b = 16

You can order 17 bulbs.

b = 17.7

0.90b0.90 =

160.90

Check:  Is the solution reasonable? You can only order whole iris bulbs. Since 18 bulbs would cost 18 • 0.90 = 16.20 plus $2.50 for shipping, which is more than $18.50, you can only order 17 bulbs.

Real World Problem for using Two-Step Equations

Step 1. Define the variable (unknown) b = number of bulbs

Step 2. Write Equation to relate cost of bulbs

.90b + 2.50 = 18.50

Step 3. Solve Equation

Modeling - Solving Two-step Equations

1. The tiles model the equation 3x – 2 = 4

2. Add 2 tiles to each side (Addition Property of Equality)

3. Remove zero pairs and divide into 3 equal groups

3x – 2 + 2 = 4 + 2

3x = 6 3 3

4. Each green tile equals two yellow tiles so …

x = 2