Solving Linear Inequalities

Anil Kumar explains how to solve linear inequalities with two examples. The video covers solving each inequality step-by-step, including multiplying to eliminate fractions, rearranging terms, and representing solutions on a number line. The video concludes with assumptions about real numbers in inequalities.

What is the first step in solving the inequality 5x + 3 divided by 2 > -1?

• Add 3 to both sides

• Divide both sides by 5

• Subtract 3 from both sides

• Multiply both sides by 2

After multiplying both sides of the inequality 5x + 3 divided by 2 > -1 by 2, what is the resulting inequality?

• 5x + 3 > -2

• 5x + 3 > 2

• 5x + 3 > 0

• 5x + 3 > -1

What is the solution for x in the inequality 5x + 3 > -2?

• x > -1

• x < -1

• x > 1

• x < 1

How is the solution x > -1 represented on a number line?

• An open circle at -1 and shading to the right

• A closed circle at -1 and shading to the right

• A closed circle at -1 and shading to the left

• An open circle at -1 and shading to the left

What is the first step in solving the inequality 5x/2 + 3 > -x - 2?

• Multiply both sides by 2

• Add x to both sides

• Divide both sides by 5

• Subtract 3 from both sides

After multiplying both sides of the inequality 5x/2 + 3 > -x - 2 by 2, what is the resulting inequality?

• 5x + 6 > -2x - 2

• 5x + 6 > x - 2

• 5x + 6 > -x - 4

• 5x + 6 > -2x - 4

What is the solution for x in the inequality 7x > -10?

• x > 10/7

• x < -10/7

• x > -10/7

• x < 10/7

How is the solution x > -10/7 represented on a number line?

• An open circle at -10/7 and shading to the left

• A closed circle at -10/7 and shading to the left

• An open circle at -10/7 and shading to the right

• A closed circle at -10/7 and shading to the right

What assumption is made about x in the context of these linear inequalities?

• x is an integer

• x is a natural number

• x is a real number

• x is a complex number