2-5 Solving Inequalities with Variables on Both Sides - PC\|MAC

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Warm Up Lesson Presentation Lesson Quiz

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Solving Inequalities with Variables on Both Sides

Warm Up

Solve each equation. 1. 2x = 7x + 15 x = ?3 2. 3y ? 21 = 4 ? 2y y = 5

3. 2(3z + 1) = ?2(z + 3) z = ?1 4. 3(p ? 1) = 3p + 2 no solution 5. Solve and graph 5(2 ? b) > 52. b < ?3

?6

?5 ?4 ?3 ?2 ?1

0

Holt McDougal Algebra 1

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Solving Inequalities with Variables on Both Sides

Objective

Solve inequalities that contain variable terms on both sides.

Holt McDougal Algebra 1

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Solving 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.

Holt McDougal Algebra 1

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Solving Inequalities with Variables on Both Sides

Example 1A: Solving Inequalities with Variables on Both Sides

Solve the inequality and graph the solutions. y 4y + 18

y 4y + 18 ?y ?y

To collect the variable terms on one side, subtract y from both sides.

0 3y + 18

?18

? 18

?18 3y

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.

?6 y (or y ?6)

?10 ?8 ?6 ?4 ?2 0 2 4 6 8 10

Holt McDougal Algebra 1

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