## Algebra 1 Student Journal 1st Edition Chapter 2 Solving Linear Inequalities

**Page 48 Essential Question Answer**

An inequality with a closed dot on the number line and a boundary point represented by the “or equal” component of the symbols ≤≤ and≥≥. The sign (∞) denotes an unlimited interval to the right. Use the symbols< for “less than” and > for “greater than” to express ordering relationships.

We can use inequalities to describe intervals on the real number line as a closed dot on the number line and a square bracket in interval notation imply inclusive inequalities with the “or equal to” component.

**Read and Learn More Big Ideas Math Algebra 1 Student Journal 1st Edition Solutions**

**Page 49 Exercise 2 Answer**

The given graph is

We represent this inequality using

x≤−6 or x>3

The required solution is x≤−6 or x>3 and graph is

The given graph is

We represent this inequality using

x<−5 or x≥4

The required solution is x<−5 or x≥4 and graph is

The given graph is

We represent this inequality using

x≤−4 or x≥5

The required solution isx≤−4 or x≥5 and graph is

The given graph is

We represent this inequality using

x<−3 or x>6

The required solution is x<−3 or x>6 and graph is

We use “or” in these inequalities to represent the union of the graph.

We use “or” in these inequalities to represent the union of the graph.

**page 49 Exercise 3 Answer**

We use combinations of inequalities to represent these graphs on the number line.

In addition, we use “and” to get the intersection of the two inequalities, and “or” to get the union of the two inequalities.

We use combinations of inequalities using “and” and “or” statements to represent these graphs on the number line.

**Page 51 Exercise 2 Answer**

Given: A number less than−2 and greater than or equal to 2.

To find Respective inequality.

Evaluate to get the answer.

We represent this inequality as follows

u<−2

u≥2

u<−2 or u≥2

The plot can be plotted as

The obtained inequality is −2<u≤2 and the plot is

**Page 51 Exercise 4 Answer**

Given: A number is more than −4 and at most \(-6 \frac{1}{2}\).

To find Respective inequality.

Evaluate to get the answer.

We represent this inequality using the following

c>−4 or c≤\(-6 \frac{1}{2}\)

The plot can be

The obtained inequality is c>−4 or c≤−\(-6 \frac{1}{2}\) and the plot is

**Page 51 Exercise 5 Answer**

Given: A number is no less than −1.5 and less than 5.3.

To find Respective inequality.

Evaluate to get the answer.

We represent this graph using the following inequalities:

c≥−1.5 and c<5.3

The plot obtained is

The obtained inequality is c≥−1.5 and c<5.3 and the plot is

**Page 52 Exercise 6 Answer**

Given: An inequality 6.4<x−3≤7.

To find The plot of the inequality.

Evaluate to get the answer.

We solve for the inequality as follows

4<x−3≤7 (Given )

4+3<x−3+3≤7+ ( Add 3 to both sides of the inequality )

7<x≤10

The plot is

The obtained inequality is 7<x≤10 and the inequality obtained is

**Page 52 Exercise 7 Answer**

Given: An inequality 15≥−5g≥−10.

To find The plot of the inequality.

Evaluate to get the answer.

We solve for the inequality as follows

15≥−5g≥−10 (Given)

\(\frac{15}{-5} \geq \frac{-5 g}{-5} \geq \frac{-10}{-5}\) (Divide both sides by −5)

-3≥g≥2 ( Inequality symbol reverse)

−3≤g≤2

The plot obtained is

The obtained inequality is −3≤g≤2 and the plot is

**Page 52 Exercise 8 Answer**

Given: An inequality z+4<2 or −3z<−27.

To find The plot of the inequality.

Evaluate to get the answer.

We solve for the inequality as follows

z+4<2 or −3z<−27 (Given)

We separate this inequality to solve for z

1.z+4<2z+4−4<2−4 (Subtract 4 on both sides)

z<−2\-3z<−27 (Divide both sides by −3)

2.\(\frac{-3 z}{-3}<\frac{-27}{-3}\)

z<9 (Inequality reverses)

z<−2 or z>9.

The plot is

The obtained inequality is −2>z>9. and the plot is

**Page 52 Exercise 9 Answer**

Given: An inequality 2t+6<10 or−t+7≤2.

To find The plot of the inequality.

Evaluate to get the answer.

We solve for the inequality as follows

2t+6<10 or −t+7≤2 (Given)

we separate this inequality to solve for t

1. 2t+6<10 (Subtract6 on both sides )

2t+6−6<10−6

2t<4

t<2

2.−t+7≤2

−t+7−7≤2−7 (Subtract both sides by 7)

−t≤−5

t≥5t<2 or t≥5.

The plot is

The obtained inequality is t≥5t<2 or t≥5. and the plot is

**Page 52 Exercise 10 Answer**

Given: An inequality \(-8 \leq \frac{1}{3}(6 x+24) \leq 12\).

To find The plot of the inequality.

Evaluate to get the answer.

Solve for the inequality as follows

\(-8 \leq \frac{1}{3}(6 x+24) \leq 12\) (Given)

\(-8 \leq \frac{1}{3}(6 x)+\frac{1}{3}(24) \leq 12 \) (Distribute and simplify)

-8≤2x+8≤24

−8−8≤2x+8−8≤24−8 & ( Subtract 8 to both sides )

−16≤2x≤16

\(\frac{-16}{2} \leq \frac{2 x}{2} \leq \frac{16}{2}\) (Divide both sides by 2)

-8≤x≤2

The plot is

The obtained inequality is −8≤x≤2. The plot obtained is

**Page 52 Exercise 11 Answer**

Given: An inequality−60≤(h−50)≤60.

To find The range of values in which the machine operates.

Evaluate to get the answer.

Let us consider and solve for h

−60≤2(h−50)≤60 (Given)

−60≤2(h)+2(−50)≤60 (Distribute )

−60≤2h−100≤60

−60+100≤2h−100+100≤60+100 (Add 100 to both sides of the inequality )

40≤2h≤160

\(\frac{40}{2} \leq \frac{2 h}{2} \leq \frac{160}{2}\) (Divide both sides by 2)

20≤h≤80.

The obtained inequality after the evaluation is 20≤h≤80.