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Correct Concepts
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MAT 101 Exam 3 Review
Consider the linear inequality 4ݔ+2ݕ<12.
Determine the boundary line of the inequality in slope-intercept form.
Will this boundary line be dashed or solid when graphing the
inequality?
Consider the linear inequality 4ݔ+2ݕ<12.
Determine the boundary line of the inequality in slope-intercept form.
ANSWER: ݕ=−2ݔ+6
Will this boundary line be dashed or solid when graphing the
inequality?
Do not erase your
ANSWER: Dashed
answers.for the next question.
You need them
Graph the solution set to the inequality 4ݔ+2ݕ<12.
Graph the solution set to the inequality 4ݔ+2ݕ<12.
Do not erase your graph. You need itfor the next
question.
Determine if the following points satisfy the inequality 4ݔ+2ݕ<12.
(1,2)
(4,1)
(-1,-3)
(-35,-40)
(100,200)
(2,2)
Determine if the following points satisfy the inequality 4ݔ+2ݕ<12.
(1,2) YES
(4,1) NO
(-1,-3) YES
(-35,-40) YES
(100,200) NO
(2,2) NO
Consider the linear inequality 3ݔ≤−6ݕ+12.
Determine the boundary line of the inequality in slope-intercept form.
Will this boundary line be dashed or solid when graphing the
inequality?
Consider the linear inequality 3ݔ≤−6ݕ+12.
Determine the boundary line of the inequality in slope-intercept form.
12
ݔ+2
ANSWER: ݕ=−
Will this boundary line be dashed or solid when graphing the
inequality?
Do not erase your
ANSWER: SOLID
answers.for the next question.
You need them
Graph the solution set to the inequality 3ݔ≤−6ݕ+12.
Graph the solution set to the inequality 3ݔ≤−6ݕ+12.
Graph the solution set to the system of linear inequalities in two
variables.
ݔ+4ݕ≥103ݔ−2ݕ<12
Graph the solution set to the system of linear inequalities in two
variables.
ݔ+4ݕ≥103ݔ−2ݕ<12
Do not erase your graph. You need it for the next question.
Useyourgraphof the solution set determinedintheprevious question to determine if the given ordered pairs are solutions to the system
ݔ+4ݕ≥103ݔ−2ݕ<12
OrderedPairs:
(6,-4)
(0,0)
(10,4)
(-3,20)
Use your graph of the solution set determined in the previous question to determine if the given ordered pairs are solutions to the system
ݔ+4ݕ≥103ݔ−2ݕ<12
OrderedPairs:
(6,-4) NO
(0,0) NO
(10,4) NO
(-3,20) YES
Determine if the following points satisfy the inequality 3ݔ≤−6ݕ+12.
(1,5)
(4,1)
(-2,3)
(-28,-1)
(100,-2)
Determine if the following points satisfy the inequality 3ݔ≤−6ݕ+12.
(1,5) NO
(4,1) NO
(-2,3) YES
(-28,-1) YES
(100,-2) NO
Solve in inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−2
−2(ݔ+1)≥4
Solve in inequality.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−2
−2(ݔ+1)≥4
ANSWER:
ݔ≥12
[12,∞)
Solve in inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
−2
ݔ−3
+4ݔ<3(ݔ+1)
Solve in inequality.
Represent your answer as an inequality, on number line, and in interval
notation.
−2
ݔ−3
+4ݔ<3(ݔ+1)
ANSWER:
ݔ>3
(3,∞)
Solve the inequality below.
Represent your answer as an inequality and in interval notation.
32
54
−2
ݔ+5
ݔ−1
<
ݔ+2
−ݔ
Solve the inequality below.
Represent your answer as an inequality and in interval notation.
32
54
−2
ݔ+5
ݔ−1
<
ݔ+2
−ݔ
ANSWER:
−563
−563
ݔ>
,∞
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
12
ݔ+4
−3<ݔ
ܣܰܦ
ݔ−1
+2ݔ≥3ݔ+5
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
12ANSWER:
ݔ+4
−3<ݔ
ܣܰܦ
ݔ−1
+2ݔ≥3ݔ+5
ݔ≥3
[3,∞)
Solve the compound inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−3
+4≤3ݔ+1
ܣܰܦ
−3
ݔ+2
+ݔ>
−2
Solve the compound inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−3
+4≤3ݔ+1
ܣܰܦ
−3
ݔ+2
+ݔ>
−2
ANSWER:
−3≤ݔ<−2
[−3,−2)
Solve the compound inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−3
<−4
ݔ+1
≥12
ܱܴ
Solve the compound inequality below.
Represent your answer as an inequality, on number line, and in interval
notation.
ݔ−3
<−4
ݔ+1
≥12
ܱܴ
ANSWER:
ݔ<1orݔ>3
−∞,1
∪[3,∞)
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
23
ݔ+2
−3ݔ<5
ݔ−3
+1≥ݔ
ܱܴ
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
23
ݔ+2
−3ݔ<5
ݔ−3
+1≥ݔ
ܱܴ
ANSWER:
ݔ<−3
−∞,−3
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
−8<4(ݔ−2)≤2(ݔ+5)
Solve the compound inequality below.
Represent your answer as an inequality, on a number line, and in
interval notation.
−8<4(ݔ−2)≤2(ݔ+5)
ANSWER:
0<ݔ≤9
(0,9]