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.
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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.