Step: 1

-5 ≤ x - 3 ≤ 2

[Original inequality.]

Step: 2

-5 + 3 ≤ x - 3 + 3 ≤ 2 + 3

[Add 3 to each ex pression.]

Step: 3

-2 ≤ x ≤ 5

[Simplify.]

Step: 4

The solution is all real numbers greater than or equal to -2 and less than or equal to 5. The graph for the solution is

Correct Answer is : Figure 2

Step: 1

-4 ≤ x -6 and x - 6 ≤ 3

[Write the inequality as two inequalities.]

Step: 2

-4 + 6 ≤ x - 6 + 6 and x - 6 + 6 ≤ 3 + 6

[Add 6 to each side.]

Step: 3

2 ≤ x and x ≤ 9

[Simplify.]

Step: 4

2 ≤ x ≤ 9

[Write compound inequality]

Step: 5

The solution is all real numbers greater than 2 and less than or equal to 9. The graph of the solution can be represented as shown below.

[The red colored region is the solution of the problem.]

Correct Answer is : Figure 1

Step: 1

- 5.5 + x < - 1.6

[Original inequality.]

Step: 2

- 5.5 + x + 5.5 < - 1.6 + 5.5

[Add 5.5 to each side.]

Step: 3

[Simplify.]

Step: 4

The solution for the inequality is the set of all real numbers less than 3.9.

Step: 5

So, among the choices, Figure 2 is the appropriate graph for the inequality.

[The set of numbers to the left of 3.9 is the solution for the inequality.]

Correct Answer is : Figure 2

Step: 1

- 2.4 + x ≤ - 5.8

[Original inequality.]

Step: 2

- 2.4 + x + 2.4 ≤ - 5.8 + 2.4

[Add 2.4 to each side.]

Step: 3

[Simplify.]

Step: 4

The solution for the inequality is set of all real numbers less than or equal to - 3.4.

Step: 5

Among the choices, Figure 4 satisfies the inequality.

Correct Answer is : Figure 4

Step: 1

[Original inequality.]

Step: 2

(6) (x 6 ) < (- 3) (6)

[Multiply each side by 6.]

Step: 3

[Simplify.]

Step: 4

The solution of the inequality includes the set of all the integers less than - 18.

Step: 5

- 18 is not included in the solution, which is represented by an open dot.

Step: 6

The region to the left of - 18 is the solution of the inequality.

[All the numbers to the left of a number are less than the number.]

Step: 7

So, the graph in figure 4 represents the inequality.

Correct Answer is : Figure 4

Step: 1

[Original inequality.]

Step: 2

[Subtract 6 from each side.]

Step: 3

[Simplify.]

Step: 4

The solution of the inequality is all real numbers greater than or equal to 5.

Step: 5

From the choice, graph 2 represents the inequality n ≥ 5.

Correct Answer is : Graph 2

Step: 1

[Original inequality.]

Step: 2

(9) (x 9 ) > (- 2) (9)

[Multiply each side by 9.]

Step: 3

[Simplify.]

Step: 4

The solution of the inequality includes the set of all the integers greater than - 18.

Step: 5

- 18 is not included in the solution, which is represented by an open dot.

Step: 6

The region to the right of - 18 is the solution of the inequality.

[All the numbers to the right of a number are greater than the number.]

Step: 7

So, the graph in Figure 1 represents the inequality.

Correct Answer is : Figure 1

Step: 1

The solution is all real numbers greater than or equal to - 3 and less than 5. The graph for the solution is:

Step: 2

So, among the choices Figure 1 is the correct choice.

Correct Answer is : Figure 1

- 6.8 +

Step: 1

- 6.8 + x > - 2.9

[Original inequality.]

Step: 2

- 6.8 + x + 6.8 > - 2.9 + 6.8

[Add 6.8 to each side.]

Step: 3

[Simplify.]

Step: 4

The solution for the inequality is the set of all real numbers greater than 3.9.

Step: 5

So, among the choices, Figure 3 is the appropriate graph for the inequality.

[The set of numbers to the right of 3.9 is the solution for the inequality.]

Correct Answer is : Figure 3

Step: 1

The solution of the inequality includes the set of all the integers less than -18.

Step: 2

The region to the left of -18 is the solution of the inequality.

[All the numbers to the right of a number are greater than the number.]

Step: 3

So, the number line in Figure 4 represents the inequality.

Correct Answer is : Figure 4

Step: 1

2x ≥ 12

[Original inequality.]

Step: 2

[Divide each side by 2.]

Step: 3

[Simplify.]

Step: 4

The inequality x ≥ 6 takes all the values greater than 6 including 6.

Step: 5

The inequalities, ≥ or ≤ are represented with closed dot on number line.

Step: 6

The following figure represents the solutions of the inequality.

Correct Answer is : Figure 2

Step: 1

3.5 + x + 5.6 ≥ 4.3

[Original inequality.]

Step: 2

[Combine like terms.]

Step: 3

[Subtract 9.1 from each side.]

Step: 4

[Simplify.]

Step: 5

Among the choices, Figure 2 satisfies the inequality.

Correct Answer is : Figure 2

- 7.7 +

Step: 1

- 7.7 + x > - 3.8

Step: 2

- 7.7 + x + 7.7 > - 3.8 + 7.7

[Add 7.7 to both sides of the equation.]

Step: 3

[Simplify.]

Step: 4

The solution for the inequality is the set of all real numbers greater than 3.9.

Step: 5

As x cannot be equal to 3.9, it should be represented by a open dot.

Step: 6

So, among the choices, Figure 3 is the appropriate graph for the inequality.

[The solution for the inequality is the set of numbers to the right of 3.9.]

Correct Answer is : Figure 3

- Converting Fractions, Decimals and Percents-Gr 7-Solved Examples
- Estimation-Whole Numbers-Gr 7-Solved Examples
- Estimation-Decimals-Gr 7-Solved Examples
- Estimation-Fractions-Gr 7-Solved Examples
- Estimation-Percentages-Gr 7-Solved Examples
- Simplifying Linear Expressions-Gr 7-Solved Examples
- Writing Linear Equations for the Situations-Gr 7-Solved Examples
- Writing Inequalities to Represent the Situations-Gr 7-Solved Examples
- Solving Two-step Linear Equations-Gr 7-Solved Examples
- Applications of Linear Equations-Gr 7-Solved Examples
- Solving Linear Inequalities - Word Problems-Gr 7-Solved Examples

- Number Line