22. Solving inequalities

Question 1

LEVEL 4

Write down the integers that satisfy the following inequality.

-4≤x<0

Select the correct answer from the list below:

A: -4,-3,-2,-1

B: -3,-2,-1

C: -4,-3,-2,-1

D: 4,3,2,1

CORRECT ANSWER:    C: -4,-3,-2,-1

WORKED SOLUTION:

Considering the inequality signs, we have a strict inequality at the top end of the range of values x can take,  meaning that x can be any value up to, but not including, 0.

At the lower end we have a non-strict inequality that means x can take,  meaning that  x can be any value down to and including, -4.

Hence the integer values  x can be are: -4,-3,-2,-1

Question 2

LEVEL 4

Solve the following inequality:

-6-7x\geq43

Select the correct answer from the list below:

A: x\leq-7

B: x\geq-7

C: x<-7

D: x>-7

CORRECT ANSWER:   A: x\leq-7

WORKED SOLUTION:

Write the inequality you want to solve                       -6-7x\geq43

Add 6 on both sides                                                -7x\geq49

Divide both sides by -7 and simplify                        x\leq-7

Question 3

LEVEL 4

Write down the numbers that satisfy the following inequality, in half increments only.

-3.5\leq x \leq -2

Select the correct answer from the list below:

A: -3,-2.5,

B: -3.5,-3,-2.5

C: -3,-2.5,-2

D: -3.5,-3,-2.5,-2

CORRECT ANSWER:  D: -3.5,-3,-2.5,-2

WORKED SOLUTION:

Considering the inequality signs, we have a non-strict inequality at the top end of the range of values x can take,  meaning that x can be any value up to, and including, -2.

At the lower end we have a non-strict inequality that means x can take,  meaning that  x can be any value down to and including, -3.5.

Hence the half integer values  x can be are: -3.5,-3,-2.5,-2

Question 4

LEVEL 4

Solve the following inequality:

6x\leq2x+10

Select the correct answer from the list below:

A: x\leq2.5

B: x<2.5

C: x\leq-2.5

D: x<-2.5

CORRECT ANSWER:    A: x\leq2.5

WORKED SOLUTION:

Write the inequality you want to solve                       6x\leq2x+10

Subtract 2x from both sides                                    4x\leq10

Divide both sides by 4                                            x\leq2.5

Question 5

LEVEL 4

Solve the following inequality:

2(x-3)>6+x

Select the correct answer from the list below:

A: x<12

B: x>12

C: x\leq 12

D: x\geq 12

CORRECT ANSWER:   B: x>12

WORKED SOLUTION:

Write the inequality you want to solve                       2(x-3)>6+x

Expand the bracket(s)                                             2x-6>6+x

Add 6 on both sides                                                2x>12+x

Subtract x from both sides                          x>12

Question 6

LEVEL 4

Solve the following inequality:

3x+5\leq14

Select the correct answer from the list below:

A: x\leq3

B: x<3

C: x>3

D: x\geq3

CORRECT ANSWER:   B: x>12

WORKED SOLUTION:

Write the inequality you want to solve                       3x+5\leq14

Subtract 5 from both sides                          3x\leq9

Divide both sides by 3 and simplify             x\leq3

Question 7

LEVEL 4

Solve the following inequality:

5-4x<37

Select the correct answer from the list below:

A: x>8

B: x<8

C: x>-8

D: x\geq-8

CORRECT ANSWER:  C: x>-8

WORKED SOLUTION:

Write the inequality you want to solve                       5-4x<37

Subtract 5 from both sides                          -4x<32

Divide both sides by -4 and simplify                        x>-8

Question 8

LEVEL 4

Solve the following inequality:

 -3(2+x)>-36

Select the correct answer from the list below:

A: x<10

B: x>10

C: x<-10

D: x\geq-10

CORRECT ANSWER: A: x<10

WORKED SOLUTION:

Write the inequality you want to solve                       -3(2+x)>-36

Expand the bracket(s)                                             -6-3x>-36

Add 6 to both sides                                                -3x>-30

Divide both sides by -3 and simplify                        x<10