PRE-ALGEBRA

PRE-ALGEBRA

Lesson 7-5 Warm-Up

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“Solving Two-Step Inequalities” (7-5)(3-1)How do you solve a

multi-step inequality?Tip: Solve a multi-step inequality exactly like an equality (equaltion with an equal sign). Isolate the variable (get the letter by itself) by:

1. “Undo”ing addition and subtraction from the variable side

2. “Undo”ing multiplication and division from the variable side

Note: If the variables is on both sides, “undo” it from one side so that there is only one variable side before doing anything else

PRE-ALGEBRA

Solve and graph 7g + 11 > 67.

7g + 11 > 67

7g + 11 – 11 > 67 – 11 Subtract 11 from each side.

7g > 56 Simplify.

g > 8 Simplify.

Solving Two-Step InequalitiesLESSON 7-5

Additional Examples

Divide each side by 7.>7g7

567

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Example: Solve 2y – 3 -5.

2y - 3 + 3 -5 + 3 Add 3 to each side.

2y + 0 -2 Simplify.

y -1 Simplify.

Check:  2y - 3 -5

2y - 3 -5 Check the direction of the inequality.

2(-2) - 3 -5 Substitute a solution less than – 1 for b like -2.

2(-1) - 3 -5 Substitute -1 for y.

-5 = -5

-7 -5 The direction of the sign is correct.

Divide each side by 2.2y2

-22

“Solving Two-Step Inequalities” (7-5)(3-1)

PRE-ALGEBRA

Example: Solve -9 – x + 6. 13

-9 – x + 6 13

-9 - 6 – x + 6 - 6 13

Add 6 to each side.

Simplify.-15 – x + 0

13

Simplify. 45 x or x 45

31– (-15)

31–

13– x

To eliminate the coefficient - from the x side, divide both sides by - which is the same as multiplying each side by the reciprocal, - When you divide or multiply both sides by a negative, reverse the direction of the inequality symbol.

13

13 3

1

Check: -9 – x + 613

-9 – (45) + 6 Substitute 45 for x.13

-9 = -9

-9 – (60) + 6 Check the direction of the inequality by substituting

x for a value bigger than 45, like 60.

13

“Solving Two-Step Inequalities” (7-5)3-1)

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Solve 6 – r – 6.< 23

6 – r – 6<23

6 + 6 – r – 6 + 6< 23

Add 6 to each side.

Simplify.12 – r< 23

Simplify.>–18 r, or r –18<

32– (12)

32–

23– r Multiply each side by . Reverse the direction of

the inequality symbol.

32

–>

Solving Two-Step InequalitiesLESSON 7-5

Additional Examples

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Dale has $25 to spend at a carnival. If the admission

to the carnival is $4 and the rides cost $1.50 each, what is

the greatest number of rides Dale can go on?

25Inequality 4 + •1.5 r <

Let = number of rides Dale goes on.

Words $4 admission + $1.50/ridenumberof rides

is less thanor equal to

$25•

r

Solving Two-Step InequalitiesLESSON 7-5

Additional Examples

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(continued)

The greatest number of rides Dale can go on is 14.

4 + 1.5r 25<

Subtract 4 from each side.4 + 1.5r – 4 25 – 4<

Simplify.1.5r 21<

Divide each side by 1.5.1.5r1.5

211.5<

Simplify.r 14<

Solving Two-Step InequalitiesLESSON 7-5

Additional Examples

PRE-ALGEBRA

Solve each inequality.

1. 14 > 4d – 10 2. + 8 7

3. 32 – 12g < 176 4. 8 + 5a 23 >

<

d < 6 k 3>

g > –12 a 3>

–k3

Solving Two-Step InequalitiesLESSON 7-5

Lesson Quiz