Solving One Step Inequalities-Gr 6-Solved Examples

Solved Examples and Worksheet for Solving One Step Inequalities

Q1Jimmy & Sunny have $12 each. Sunny spends $5 on jellybeans, while Jimmy spends less on jellybeans. Which of the inequalities describes the money m left with Jimmy?
A. m > 12
B. m > 7
C. m ≥ 12
D. m < 7

Solutions

Step: 1

Out of $12, Sunny spends $5 while Jimmy spends less than $5.

[From the problem.]

Step: 2

Sunny has $7 left with him and Jimmy has more than $7.

[Money left = money initially had - money spent.]

Step: 3

So, the inequality for the money left with Jimmy is m > 7.

[m is the money left with Jimmy.]

Correct Answer is : m > 7

Q2Sheela had more than $87 in her savings account. She withdrew $59 from her savings account. Which of the following inequalities best suits the balance amount m, in her savings account?
A. m ≤ 28
B. m < 28
C. m ≥ 28
D. m > 28

Solutions

Step: 1

Sheela withdrew $59 from her savings account, which had more than $87.

Step: 2

The balance amount in her savings bank account will be more than 87 - 59= $28.

Step: 3

The inequality for the balance amount m is m > 28.

Correct Answer is : m > 28

Q3Andy delivers bread packets to more than 66 families living in Dugway each day. Which of the following inequalities best describes the situation?
A. b ≤ 66
B. b > 66
C. b < 66
D. b ≥ 66

Solutions

Step: 1

Let b be the bread packets delivered to the families living in Dugway.

Step: 2

Bread packets b, that Andy delivers to families living in Dugway are more than 66.

Step: 3

The inequality is b > 66.

Correct Answer is : b > 66

Q4Jeff bought a pair of Guess jeans, which cost less than $50. Which of the following inequalities best describes the situation when the cost price is represented by p?

A. p ≤ 50
B. p < 50
C. p > 50
D. p ≥ 50

Solutions

Step: 1

Jeff bought a Guess jeans that costs less than $50.

Step: 2

The inequality is p < 50.

Correct Answer is : p < 50

Q5Which of the following is a solution for the inequality below?
10.7 + x > 4.5
A. - 8.2
B. - 7.2
C. - 5.7
D. - 9.2

Solutions

Step: 1

10.7 + x > 4.5

[Given inequality.]

Step: 2

10.7 + x - 10.7 > 4.5 - 10.7

[Subtract 10.7 from each side.]

Step: 3

x > - 6.2

[Simplify.]

Step: 4

The solution for the inequality is, all real numbers greater than - 6.2.

Step: 5

From the choices, the solution greater than - 6.2 is - 5.7.

Correct Answer is : - 5.7

Q6Which of the following is a solution for the inequality? - 3.7 + x < - 4.5

A. -0.7
B. 0.9
C. -0.9
D. 0.1

Solutions

Step: 1

- 3.7 + x < - 4.5

[Original inequality.]

Step: 2

- 3.7 + x + 3.7 < - 4.5 + 3.7

[Add 3.7 to each side.]

Step: 3

x < -0.8

[Simplify.]

Step: 4

The solution for the inequality is, all real numbers less than -0.8.

Step: 5

Among the choices, the solution for the inequality is -0.9 .

Correct Answer is : -0.9

Q7Which of these is a solution for the inequality below?
x + 3.5 ≥ 6.8
A. 3.1
B. 3.4
C. 3.0
D. 3.2

Solutions

Step: 1

x + 3.5 ≥ 6.8

[Original inequality.]

Step: 2

x + 3.5 - 3.5 ≥ 6.8 - 3.5

[Subtract 3.5 from each side.]

Step: 3

x ≥ 3.3

[Simplify.]

Step: 4

The solution for the inequality is, all real numbers greater than or equal to 3.3.

Step: 5

From the choices, the solution for the inequality is 3.4.

Correct Answer is : 3.4

Q8Which of the following is a solution for the inequality x + 8.5 ≤ 3.8?

A. -4.7
B. -4.4
C. -4.5
D. -4.3

Solutions

Step: 1

x + 8.5 ≤ 3.8

[Original inequality.]

Step: 2

x + 8.5 - 8.5 ≤ 3.8 - 8.5

[Subtract 8.5 from each side.]

Step: 3

x ≤ -4.7

[Simplify.]

Step: 4

The solution for the inequality is, all real numbers less than or equal to -4.7.

Step: 5

From the choices, the solution for the inequality is -4.7.

Correct Answer is : -4.7

Q9There were fewer than 10 students in an English class. Which of the following inequalities best describes the situation when the number of students is represented by s?
A. s ≥ 10
B. s < 10
C. s > 10
D. s ≤ 10

Solutions

Step: 1

There were fewer than 10 students in an English class.

Step: 2

The number of students is represented by s.

Step: 3

The inequality is s < 10.

Correct Answer is : s < 10

Q10Annie had less than $106 in her savings account. She withdrew $68 from her savings account. Which of the following inequalities best suits the balance amount m, in her savings account?
A. m ≤ 38
B. m > 38
C. m ≥ 38
D. m < 38

Solutions

Step: 1

Annie withdrew $68 from her savings account, which had less than $106.

Step: 2

The balance amount in her savings bank account will be less than 106 - 68 = $38.

Step: 3

The inequality for the balance amount m is m < 38.

Correct Answer is : m < 38

Q11Which of the following is not a solution of the inequality, x - 7 ≤ 2?
A. 8
B. 9
C. 7
D. 10

Solutions

Step: 1

x - 7 ≤ 2

[Original inequality.]

Step: 2

x - 7 + 7 ≤ 2 + 7

[Add 7 to both sides.]

Step: 3

x ≤ 9

[Simplify.]

Step: 4

Any real number, which is less than or equal to 9, is a solution for the inequality.

Step: 5

From the choices, 10 is the number which is not a solution of the inequality.

[10 is greater than 9.]

Correct Answer is : 10

Q12Choose a solution for the inequality, x - 2 ≥ 49.
A. 41
B. 49
C. 51
D. 46

Solutions

Step: 1

x - 2 ≥ 49

[Original inequality.]

Step: 2

x - 2 + 2 ≥ 49 + 2

[Add 2 to each side.]

Step: 3

x ≥ 51

[Simplify.]

Step: 4

The solution for the inequality is, all real numbers greater than or equal to 51.

Step: 5

From the choice, 51 is the correct answer.

Correct Answer is : 51

Q13Which of the following is a solution for the inequality x + 3 ≥ 4?
A. -1
B. -2
C. 0
D. 1

Solutions

Step: 1

x + 3 ≥ 4

[Original inequality.]

Step: 2

x + 3 - 3 ≥ 4 - 3

[Subtract 3 from each side.]

Step: 3

x ≥ 1

[Simplify.]

Step: 4

All real numbers greater than or equal to 1.

Step: 5

From the choices, the number greater than or equal to 1 is 1.

Correct Answer is : 1

Q14Which of the choices represents the solution for the inequality, 9x > 81?
A. x < 9
B. x > 9
C. x ≥ 9
D. x ≤ 9

Solutions

Step: 1

9x > 81

[Original inequality.]

Step: 2

9x9 > 819

[Divide by 9 on both sides, according to division property, if c > 0 and a > b then ac > bc.]

Step: 3

x > 9

[Simplify.]

Correct Answer is : x > 9

Q15Choose the correct mathematical expression for the verbal description.

M is less than 6 times the value of 15 the height, where the height is H
A. M < 15H
B. M < 6 (15H)
C. M = 6 (15H)
D. M > 6 (15H)

Solutions

Step: 1

The value of 15 the height = 15H

Step: 2

6 times the value of 15 the height = 6(15H)

Step: 3

M is less than 6 times the value of 15 the height can be written as M < 6(15H)

Correct Answer is : M < 6 (15H)

Solved Examples and Worksheet for Solving One Step Inequalities

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HighSchool Math