Question 1

Solve the inequality $$6x - 13 \u003c 5x - 8$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 5]$$

Question 2

Which property is used when subtracting $$5x$$ from both sides of the inequality $$6x - 13 \u003c 5x - 8$$?

Accepted Answer

Subtraction property of inequality

Question 3

If you solve $$x - 13 \leq -8$$, what is the value of $$x$$?

Accepted Answer

$$x \leq 5$$

Question 4

Which of the following correctly describes the interval notation for $$x \u003c 7$$?

Accepted Answer

$$(-\infty, 7)$$

Question 5

A chemical process requires the temperature $$T to be at $$most $$120$$ degrees. Which inequality and interval notation represent this requirement?

Accepted Answer

$$T \leq 120$$, $$(-\infty, 120]$$

Question 6

Which of the following is true about the endpoint in the interval $$(-\infty, 5]$$?

Accepted Answer

The endpoint 5 is included.

Question 7

A medication is safe if the dosage $$d$$ satisfies $$d \leq 250 mg. $$Which graph best represents the solution?

Accepted Answer

A number line shaded to the left of 250 with a closed circle at 250

Question 8

Which of the following is the correct solution to $$4x + 7 \leq 19$$?

Accepted Answer

$$x \leq 3$$

Question 9

If $$x$$ represents the number of hours a student can work and the maximum allowed is 20 hours, which inequality and interval notation represent this situation?

Accepted Answer

$$x \leq 20$$, $$(-\infty, 20]$$

Question 10

Which of the following is the correct interval notation for all real numbers less than or equal to $$-3$$?

Accepted Answer

$$(-\infty, -3]$$

Question 11

A historical event occurred before the year 1900. Which inequality and interval notation represent all years $$y$$ before 1900?

Accepted Answer

$$y \u003c 1900$$, $$(-\infty, 1900)$$

Question 12

Which of the following statements is true about the interval $$(-\infty, 5]$$?

Accepted Answer

It includes all real numbers less than or equal to 5.

Question 13

If $$x is a $$solution to $$x - 13 \leq -8$$, which of the following must be true?

Accepted Answer

$$x is $$less than or equal to 5

Question 14

A company policy states that employees must be at least 18 years old. Which inequality and interval notation represent this requirement?

Accepted Answer

$$x \geq 18$$, $$[18, \infty)$$

Question 15

Which of the following is the correct solution to $$7x - 2 \u003c 5x + 8$$?

Accepted Answer

$$x \u003c 5$$

Solving and Graphing Linear Inequalities in One Variable

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