holt mcdougal algebra 1 solving inequalities by adding or subtracting solving inequalities by adding...

Holt McDougal Algebra 1

Solving Inequalities by Adding or Subtracting


Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz




Warm UpGraph each inequality. Write an inequality for each situation. 1. The temperature must be at least –10°F.

2. The temperature must be no more than 90°F.

x ≥ –10

x ≤ 90

Solve each equation.

3. x – 4 = 10 14

4. 15 = x + 1.1 13.9

–10 0 10

–90 0 90



Solve one-step inequalities by using addition.

Solve one-step inequalities by using subtraction.

Objectives



Solving one-step inequalities is much like solving one-step equations. To solve an inequality, you need to isolate the variable using the properties of inequality and inverse operations.



Helpful Hint

Use an inverse operation to “undo” the operation in an inequality. If the inequality contains addition, use subtraction to undo the addition.



a. s + 1 ≤ 10

Check It Out! Example 1

–1– 1 s + 0 ≤ 9

s ≤ 9

Since 1 is added to s, subtract 1 from both sides to undo the addition.

b. > –3 + t

Since –3 is added to t, add 3 to both sides to undo the addition.

Solve each inequality and graph the solutions.

s + 1 ≤ 10

> –3 + t

+3 +3

> 0 + t

t <

9

–10 –8 –6 –4 –2 0 2 4 6 8 10

–10 –8 –6 –4 –2 0 2 4 6 8 10



q – 3.5 < 7.5

+3.5 +3.5

q – 0 < 11

q < 11

Since 3.5 is subtracted from q, add 3.5 to both sides to undo the subtraction.

Check It Out! Example 1c

Solve the inequality and graph the solutions.

q – 3.5 < 7.5

–7 –5 –3 –1 1 3 5 7 9 11 13



Since there can be an infinite number of solutions to an inequality, it is not possible to check all the solutions. You can check the endpoint and the direction of the inequality symbol.

The solutions of x + 9 < 15 are given by x < 6.




The Recommended Daily Allowance (RDA) of iron for a female in Sarah’s age group (14-18 years) is 15 mg per day. Sarah has consumed 11 mg of iron today. Write and solve an inequality to show how many more milligrams of iron Sarah can consume without exceeding RDA.



Check It Out! Example 2 Continued

Understand the problem11

The answer will be an inequality and a graph that show all the possible amounts of iron that Sarah can consume to reach the RDA.

List important information:

• The RDA of iron for Sarah is 15 mg.

• So far today she has consumed 11 mg.



22 Make a Plan

Write an inequality.

Let x represent the amount of iron Sarah needs to consume.

Amount taken plus 15 mgis at

mostamount needed

11 + x 15

11 + x 15




Solve33

Since 11 is added to x, subtract 11 from both sides to undo the addition.

11 + x 15

x 4

Draw a solid circle at 4.Shade all numbers less than 4.

0 1 2 3 4 5 6 7 8 9 10

x 4. Sarah can consume 4 mg or less of iron without exceeding the RDA.


–11 –11



Look Back44

Check

Check the endpoint, 4.

11 + x = 15

11 + 4 1515 15

Sarah can consume 4 mg or less of iron without exceeding the RDA.

Check a number less than 4.

11 + 3 15

11 + 3 1514 15





What if…? Josh wants to try to break the school bench press record of 282 pounds. He currently can bench press 250 pounds. Write and solve an inequality to determine how many more pounds Josh needs to lift to break the school record. Check your answer.

Let p represent the number of additional pounds Josh needs to lift.

250 pounds plus additional pounds is greater than

282 pounds.

250 + p > 282




CheckCheck the endpoint, 32.

250 + p = 282

250 + 32 282282 282

Check a number greater than 32.

250 + p > 282

250 + 33 > 282283 > 282

Josh must lift more than 32 additional pounds to reach his goal.

250 + p > 282–250 –250

p > 32

Since 250 is added to p, subtract 250 from both sides to undo the addition.



Lesson Quiz: Part I

Solve each inequality and graph the solutions.

1. 13 < x + 7

x > 6

2. –6 + h ≥ 15h ≥ 21

3. 6.7 + y ≤ –2.1

y ≤ –8.8



Lesson Quiz: Part II

4. A certain restaurant has room for 120 customers. On one night, there are 72 customers dining. Write and solve an inequality to show how many more people can eat at the restaurant. x + 72 ≤ 120; x ≤ 48, where x is a natural number

holt mcdougal algebra 1 solving inequalities by adding or subtracting solving inequalities by adding...

Documents