Question 1

Which of the following is a linear inequality in one variable?

Accepted Answer

A linear inequality in one variable is an inequality that involves a linear expression in one variable and uses inequality symbols like , =. Among the choices, 2x + 3

Question 2

The solution set of the inequality 3x - 5

Accepted Answer

Solving 3x - 5

Question 3

If -3x > 9, then:

Accepted Answer

When both sides of an inequality are divided or multiplied by a negative number, the sign of inequality is reversed. Dividing -3x > 9 by -3 gives x

Question 4

The solution of the inequality 5x - 3 >= 3x - 5 in interval notation is:

Accepted Answer

Solving 5x - 3 >= 3x - 5: subtract 3x from both sides to get 2x - 3 >= -5, then add 3 to get 2x >= -2, which gives x >= -1. In interval notation, this is represented as -1, infinity).

Question 5

Which of the following points lies in the half-plane represented by 2x + 3y > 6?

Accepted Answer

Substitute the coordinates of each point into the inequality 2x + 3y > 6. For (2, 1): 2(2) + 3(1) = 4 + 3 = 7, which is > 6. Thus, (2, 1) satisfies the inequality and lies in the half-plane.

Linear Inequalities