Solving Linear Inequalities with Addition and Subtraction

The video tutorial introduces inequalities, explaining the difference between equations and inequalities. It demonstrates solving inequalities through examples, including x - 5 < 35, x + 15 ≥ -60, x - 2 ≤ 1, and x - 32 ≤ 0. Each example is solved step-by-step, and the solution is visualized on a number line. The tutorial emphasizes understanding the notation and solution sets of inequalities.

What is the solution for the inequality x - 5 < 35?

• x < 45

• x < 30

• x < 35

• x < 40

On a number line, how is the point x = 40 represented for the inequality x < 40?

• Filled circle at 40

• Open circle at 40

• Line at 40

• Shaded area starting at 40

Which of the following is a correct representation of an inequality solution on a number line for x < 40?

• Filled circle at 40 with shading to the left

• Open circle at 40 with shading to the left

• Filled circle at 40 with shading to the right

• Open circle at 40 with shading to the right

What does x + 15 ≥ -60 simplify to when solved?

• x ≥ -75

• x ≥ -45

• x ≥ -60

• x ≥ -70

In the inequality x + 15 ≥ -60, how is x = -75 represented on a number line?

• Filled circle at -75

• Open circle at -75

• Line at -75

• No circle at -75

If x + 15 is greater than or equal to -60, which of the following is a possible value of x?

• -85

• -75

• -55

• -65

What is the solution for the inequality x - 2 ≤ 1?

• x ≤ 1

• x ≤ 2

• x ≤ 4

• x ≤ 3

How is the solution x ≤ 3 represented on a number line for the inequality x - 2 ≤ 1?

• Shaded area starting at 3

• Open circle at 3

• Filled circle at 3

• Line at 3

What does the inequality x - 32 ≤ 0 simplify to?

• x ≤ 30

• x ≤ 34

• x ≤ 32

• x ≤ 28

For the inequality x - 32 ≤ 0, how is the solution x = 32 represented on a number line?

• Line at 32

• Filled circle at 32

• No circle at 32

• Open circle at 32