Go through the **Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.8 Solving Inequalities**Â 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 â‰¤ or â‰Ą, 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

Answer:

Given Linear inequality Equation isÂ 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 > zÂ – 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

Answer:

Given Linear inequality Equation isÂ 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

Answer:

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

Answer:

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

Answer:

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

Answer:

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 â‰¤ 8 + r

Answer:

Given Linear inequality Equation is 8 â‰¤ 8 + r

Now Add -8 on both the sides in order to segregate the variable on single side of an inequality stated.

8 â‰¤ 8 + r

8 – 8 â‰¤ 8 + r – 8

0 â‰¤ r

r â‰Ą 0

Therefore after simplification r represents a value greater than Equal to zeroÂ .

Now indicate the number on the number line by placing an closed circle on zero which is as shown below.

Question 8.

w + 8 â‰Ą 11

Answer:

Given Linear inequality Equation is w + 8 â‰Ą 11

Now Add -8 on both the sides in order to segregate the variable on single side of an inequality stated.

w + 8 – 8 â‰Ą 11 – 8

w + 0 â‰Ą 11 – 8

w â‰Ą 11 – 8

w â‰Ą 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

Answer:

Given Linear inequality Equation isÂ 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

Answer:

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

Answer:

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

Answer:

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 â‰Ą -6

Answer:

Given Linear inequality Equation 6 + s â‰Ą -6

Now Add -6 on both the sides in order to segregate the variable on single side of an inequality stated.

6 + s – 6 â‰Ą – 6 – 6

0 + s â‰Ą -6 – 6

sÂ â‰Ą -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 â‰Ą 8

Answer:

Given Linear inequality Equation f + 2 â‰Ą 8

Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.

f + 2 – 2 â‰Ą 8 -2

f + 0Â â‰Ą 8 -2

fÂ â‰Ą 8 -2

fÂ â‰Ą 6

Therefore after simplification f represents a value greater than 6Â .

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

Answer:

Given Linear inequality Equation f + 2 â‰Ą 8

Now Add -2 on both the sides in order to segregate the variable on single side of an inequality stated.

f + 2 – 2 â‰Ą 8 -2

f + 0Â â‰Ą 8 -2

fÂ â‰Ą 8 -2

fÂ â‰Ą 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 â‰¤ 9

Answer:

Given Linear inequality Equation -3 + g â‰¤ 9

Now Add 3 on both the sides in order to segregate the variable on single side of an inequality stated.

-3 + 3 + g â‰¤ 9 +3

0 + g â‰¤ 9 +3

g â‰¤ 9 +3

g â‰¤ 12

Therefore after simplification g represents a value less than or Equal to 12 .

Now indicate the number on the number line by placing an closed circle on 12 which is as shown below.