algebra 1 lesson 3-4 warm-up. algebra 1 lesson 3-4 warm-up

ALGEBRA 1

Lesson 3-4 Warm-Up

ALGEBRA 1

“Solving Multi-Step Inequalities” (3-4)(3-1)How do you solve a

multi-step inequality?Tip: Solve a multi-step inequality exactly like an equality (equation 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

ALGEBRA 1

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)

ALGEBRA 1

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 Multi-Step Inequalities” (3-4)-1)

ALGEBRA 1

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

ALGEBRA 1

Solve 5 + 4b < 21.

5 + 4b – 5 < 21 – 5 Subtract 5 from each side.

4b < 16 Simplify.

b < 4 Simplify.

Check: 5 + 4b = 21 Check the computation.

5 + 4b < 21 Check the direction of the inequality.

5 + 4(3) < 21 Substitute 3 for b.

5 + 4(4) 21 Substitute 4 for b.

21 = 21

17 < 21

< Divide each side by 4.4b4

164

Solving Multi-Step InequalitiesLESSON 3-4

Additional Examples

ALGEBRA 1

The band is making a rectangular banner that is 20 feet

long with trim around the edges. What are the possible widths

the banner can be if there is no more than 48 feet of trim?

twice the the length length of the trim

Words: plustwice the

widthcan be nomore than

Equation: 2(20) + 2w 48<


Additional Examples

ALGEBRA 1

(continued)

The banner’s width must be 4 feet or less.

2(20) + 2w 48<

40 + 2w 48 Simplify 2(20).<

40 + 2w – 40 48 – 40 Subtract 40 from each side.<

2w 8 Simplify.<

w 4 Simplify.<

Divide each side by 2.<2w2

82


Additional Examples

ALGEBRA 1

Solve 3x + 4(6 – x) < 2.

3x + 24 – 4x < 2 Use the Distributive Property.

–x + 24 < 2 Combine like terms.

–x + 24 – 24 < 2 – 24 Subtract 24 from each side.

–x < –22 Simplify.

x > 22 Simplify.

> Divide each side by –1. Reverse the inequality symbol.

–x–1

–22–1


Additional Examples

ALGEBRA 1

a.) Solve 8z – 6 < 3z + 12.

8z – 6 – 3z < 3z + 12 – 3z “Undo” the variable from one side first by subtracting 3z from each side.

5z – 6 < 12 Combine like terms.

5z – 6 + 6 < 12 + 6 Add 6 to each side.

5z < 18 Simplify.

< Divide each side by 5.5z5

185

z < 3 Simplify.35


Additional Examples

ALGEBRA 1

b.) Solve 5(–3 + d) 3(3d – 2).<

–15 – 4d + 15 –6 + 15 Add 15 to each side. <

–4d 9 Simplify.<

–15 + 5d – 9d 9d – 6 – 9d Subtract 9d from each side. <

–15 – 4d –6 Combine like terms.<

–15 + 5d 9d – 6 Use the Distributive Property.<

d –2 Simplify.>14

Divide each side by –4. Reverse the inequality symbol.

–4d–4

9 –4>


Additional Examples

ALGEBRA 1

Solve each inequality.

1. 8 + 5a 23 2. – p < p – 6

3. 3(x – 4) > 4x + 7 4. 3(3c + 2) 2(3c – 2)

>

<

13

12

a 3> p > 7 15

x < –19 <c –313


Lesson Quiz

algebra 1 lesson 3-4 warm-up. algebra 1 lesson 3-4 warm-up

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