# Spectrum Math Grade 6 Chapter 5 Lesson 8 Answer Key Solving Inequalities

Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.8 Solving Inequalities and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 5 Lesson 5.8 Solving Inequalities Answers Key

Inequalities can be solved the same way that equations are solved.
6 + q > 14 1. Subtract 6 from both sides of the inequality to isolate the variable on one side of the inequality.
6 + q – 6 > 14 – 6
q > 8 2. The variable q represents a value that is greater than 8. A number line can be used to represent the possible values of the variable. An open circle shows that the values do not include 8. For inequalities that use ≤ or ≥, a closed circle indicates that the values do include that point.

Solve the inequalities and represent the possible values of the variable on a number line.

Question 1.
6 > z – 2
Given Linear inequality Equation is  6 > z – 2.
Now Add 2 on both the sides in order to segregate the variable on single side of an inequality stated.
6 + 2 > z – 2 + 2
4 > z  – 0
4 > z
z < 4
Therefore after simplification z represents a value less than 4.
Now indicate the number on the number line by placing an open circle on 4 which is as shown below. Question 2.
g + 7 < -12
Given Linear inequality Equation is  g + 7 < -12
Now Add -7 on both the sides in order to segregate the variable on single side of an inequality stated.
g + 7 -7 < -12 – 7
g – 0 < -19
g < -19
Therefore after simplification g represents a value less than -19.
Now indicate the number on the number line by placing an open circle on -19 which is as shown below. Question 3.
d – 5 < 7
Given Linear inequality Equation is d – 5 < 7
Now Add 5 on both the sides in order to segregate the variable on single side of an inequality stated.
d – 5 < 7 +5
d – 5 + 5 < 7 +5
d – 0 < 12
d < 12
Therefore after simplification d represents a value less than 12.
Now indicate the number on the number line by placing an open circle on 12 which is as shown below. Question 4.
15 > k + 2
Given Linear inequality Equation is 15 > k + 2
Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.
15 – 2 > k + 2 – 2
13 > k + 0
13 > k
k < 13
Therefore after simplification k represents a value less than 13.
Now indicate the number on the number line by placing an open circle on 13 which is as shown below. Question 5.
1 + x > -16
Given Linear inequality Equation is 1 + x > -16
Now Add -1 on both the sides in order to segregate the variable on single side of an inequality stated.
1 + x – 1 > -16 – 1
x + 0 > -17
x > -17
Therefore after simplification x represents a value Greater than -17.
Now indicate the number on the number line by placing an open circle on -17 which is as shown below. Question 6.
y + 8 < -9
Given Linear inequality Equation is y + 8 < -9
Now Add -8 on both the sides in order to segregate the variable on single side of an inequality stated.
y + 8 < -9
y + 8 – 8 < -9 – 8
y + 0 < -17
y < -17
Therefore after simplification y represents a value Less than -17.
Now indicate the number on the number line by placing an open circle on -17 which is as shown below. Question 7.
8 ≤ 8 + r
Given Linear inequality Equation is 8 ≤ 8 + r
Now Add -8 on both the sides in order to segregate the variable on single side of an inequality stated.
8 ≤ 8 + r
8 – 8 ≤ 8 + r – 8
0 ≤ r
r ≥ 0
Therefore after simplification r represents a value greater than Equal to zero  .
Now indicate the number on the number line by placing an closed circle on zero which is as shown below. Question 8.
w + 8 ≥ 11
Given Linear inequality Equation is w + 8 ≥ 11
Now Add -8 on both the sides in order to segregate the variable on single side of an inequality stated.
w + 8 – 8 ≥ 11 – 8
w + 0 ≥ 11 – 8
w ≥ 11 – 8
w ≥ 3
Therefore after simplification w represents a value greater than Equal to 3.
Now indicate the number on the number line by placing an closed circle on 3 which is as shown below. Solve the inequalities and represent the possible values of the variable on a number line.

Question 1.
x – 2 < 12
Given Linear inequality Equation is  x – 2 < 12
Now Add 2 on both the sides in order to segregate the variable on single side of an inequality stated.
x – 2 + 2< 12 + 2
x + 0 < 14
x < 14
Therefore after simplification x represents a value less than 14.
Now indicate the number on the number line by placing an open circle on 14 which is as shown below. Question 2.
-1 + y > 17
Given Linear inequality Equation -1 + y > 17
Now Add 2 on both the sides in order to segregate the variable on single side of an inequality stated.
-1 + y + 1 > 17 + 1
y + 0 > 17 + 1
y > 17 + 1
y > 18
Therefore after simplification y represents a value Greater than 18.
Now indicate the number on the number line by placing an open circle on 18 which is as shown below. Question 3.
p + 2 < -13
Given Linear inequality Equation p + 2 < -13
Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.
p + 2 < -13
p + 2 – 2 < -13 – 2
p + 0 < -15
p < -15
Therefore after simplification p represents a value Lesser than 15.
Now indicate the number on the number line by placing an open circle on 15 which is as shown below. Question 4.
-7 + v < -17
Given Linear inequality Equation -7 + v < -17
Now Add 7 on both the sides in order to segregate the variable on single side of an inequality stated.
-7 + v < -17
-7 + 7 + v < -17 + 7
0 + v < -17 + 7
v < -10
Therefore after simplification v represents a value Lesser than -10.
Now indicate the number on the number line by placing an open circle on -10 which is as shown below. Question 5.
6 + s ≥ -6
Given Linear inequality Equation 6 + s ≥ -6
Now Add -6 on both the sides in order to segregate the variable on single side of an inequality stated.
6 + s – 6 ≥ – 6 – 6
0 + s ≥ -6 – 6
s  ≥ -12
Therefore after simplification s represents a value greater than 12 .
Now indicate the number on the number line by placing an closed circle on 12 which is as shown below. Question 6.
f + 2 ≥ 8
Given Linear inequality Equation f + 2 ≥ 8
Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.
f + 2 – 2 ≥ 8 -2
f + 0  ≥ 8 -2
f  ≥ 8 -2
f  ≥ 6
Therefore after simplification f represents a value greater than 6  .
Now indicate the number on the number line by placing an closed circle on 6 which is as shown below. Question 7.
-10 > w – 1
Given Linear inequality Equation f + 2 ≥ 8
Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.
f + 2 – 2 ≥ 8 -2
f + 0  ≥ 8 -2
f  ≥ 8 -2
f  ≥ 6
Therefore after simplification f represents a value greater than or Equal to 6 .
Now indicate the number on the number line by placing an closed circle on 6 which is as shown below. Question 8.
-3 + g ≤ 9 