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Pearson Algebra 1 Common Core, 2011 View details

1. Inequalities and Their Graphs

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Exercise 2 Page 167

Practice makes perfect

By substituting x=-1 into the inequality, we can check whether the inequality holds true.

6x-3≥10

Substitute

x= -1

6( -1)-3? ≥10

MultPosNeg

a(- b)=- a * b

-6*1-3? ≥10

MultByOne

a * 1=a

-6-3? ≥10

SubTerm

Subtract term

-9 ≱ 10

A negative number cannot be greater than or equal to a positive number. Therefore, x=-1 is not a solution to the inequality.

Let's do the same thing again and substitute x=0 into the inequality.

6x-3≥10

Substitute

x= 0

6( 0)-3? ≥10

ZeroPropMult

Zero Property of Multiplication

0-3? ≥10

SubTerm

Subtract term

-3≱ 10

Again, a negative number cannot be greater than or equal to a positive number. Hence, x=0 is not a solution to the inequality.

Let's substitute x=3 into the inequality and check its validity.

6x-3≥10

Substitute

x= 3

6( 3)-3? ≥10

Multiply

18-3? ≥10

SubTerm

Subtract term

15≥10

Since 15 is greater than 10 the inequality is true. This means that x=3 is a solution.

Let's substitute x=4 into the inequality and check its validity.

6x-3≥10

Substitute

x= 4

6( 4)-3? ≥ 10

Multiply

24-3? ≥0

SubTerm

Subtract term

21≥10

Since 21 is greater than 10 the inequality holds true. This means that x=4 is a solution.

Extra

Solutions of the Inequality

We found that two of the values given in the exercise are solutions of the inequality. Now, let's consider if theses two numbers are the only solutions. First, we need to simplify the inequality using the Properties of Inequality.

6x-3 ≥ 10

AddIneq

LHS+3≥RHS+3

6x ≥ 13

DivIneq

.LHS /6.≥.RHS /6.

x ≥ 13/6

We simplified the inequality. Next, to help us visualize the problem we will draw the inequality on the number line. Let's take a look.