3-5 solving inequalities with variables on both...

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

3-5Solving Inequalities with Variables on Both Sides

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Section 3-5 1

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Bell Quiz 3-5

Solve each equation.

1. 2x = 7x + 15

2. Solve and graph 5(2 – b) > 52.

5 pts

possible

2 pts

3 pts

Section 3-5 2

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Questions on 3-4

Section 3-5 3

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Solve inequalities that contain variable terms on both sides.

Objective

Section 3-5 4

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Some inequalities have variable terms on both sides of the inequality symbol. You can solve these inequalities like you solved equations with variables on both sides.

Use the properties of inequality to “collect” all the

variable terms on one side and all the constant terms on the other side.

Section 3-5 5

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

3 STEPS TO SOLVING

1. SimPlify = PEMDAS (LHS/RHS)

2. “Collect” variables

3. Solve = SADMEP

Section 3-5 6

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Example 1A: Solving Inequalities with Variables on

Both SidesSolve the inequality and graph the solutions.

y ≤ 4y + 18 To collect the variable terms on one side, subtract y from both sides.

Since 18 is added to 3y, subtract 18 from both sides to undo the addition.

Since y is multiplied by 3, divide both sides by 3 to undo the multiplication.

Section 3-5 7

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

4m – 3 < 2m + 6 To collect the variable terms on one side, subtract 2m from both sides.

Since 3 is subtracted from 2m, add 3 to both sides to undo the subtraction

Since m is multiplied by 2, divide both sides by 2 to undo the multiplication.

Example 1B: Solving Inequalities with Variables on

Both Sides

Solve the inequality and graph the solutions.

Section 3-5 8

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Solve the inequality and graph the solutions.Check It Out! Example 1

1a: 4x ≥ 7x - 6

1b: 5t + 1 < –2t – 6

Section 3-5 9

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Skip Example 2

Section 3-5 10

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

You may need to simplify one or both sides of an inequality before solving it. Look for liketerms to combine and places to use the Distributive Property.

Section 3-5 11

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Example 3A: Simplify Each Side Before Solving Solve the inequality and graph the solutions.

2(k – 3) > 6 + 3k – 3

Distribute 2 on the left side of the inequality.

To collect the variable terms, subtract 2k from both sides.

Since 3 is added to k,

subtract 3 from

both sides to undo

the addition. Section 3-5 12

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Example 3B: Simplify Each Side Before Solving

Solve the inequality and graph the solution.

0.9y ≥ 0.4y – 0.5

To collect the variable terms, subtract 0.4y from both sides.

Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication.

Section 3-5 13

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Check It Out! Example 3Solve the inequality and graph the solutions.

3a: 5(2 – r) ≥ 3(r – 2)

3b: 0.5x – 0.3 + 1.9x < 0.3x + 6

Section 3-5 14

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

There are special cases of inequalities called identities and contradictions.

Section 3-5 15

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Section 3-5 16

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

Example 4A: Identities and Contradictions

Solve the inequality.

2x – 7 ≤ 5 + 2xSubtract 2x from both sides.

The inequality 2x − 7 ≤ 5 + 2x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions. 17

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

2(3y – 2) – 4 ≥ 3(2y + 7)

Distribute 2 on the left side

and 3 on the right side.

Example 4B: Identities and Contradictions

Solve the inequality.

Subtract 6y from both sides.

No values of y make the inequality true. There are no solutions.18

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

4a: 4(y – 1) ≥ 4y + 2

Check It Out! Example 4

Solve the inequality.

4b: x – 2 < x + 1

Section 3-5 19

Holt Algebra 1

3-5Solving Inequalities with Variables on Both Sides

HOMEWORKSec 3-5: (Pg 197) 3, 7, 10, 14, 15, 21, 24, 25, 28, 30, 31, 34, 36, 37, 41, 43, 44, 52, 53 (14, 15, 36, 37, 52, 53 DO NOT need graphs; all other problems DO need graphs. Graphsare due in 2 class periods on paper. Still type inequality answers in online.)

Section 3-5 20