Question 1

Which of the following is the correct interval notation for the solution set $$\{x|x \geq 3\}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

Solve the inequality $$2x - 5 \geq 6x + 3$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, -2]$$

Question 3

Which of the following inequalities represents the phrase: 'The temperature is at most 20 degrees'?

Accepted Answer

$$x \leq 20$$

Question 4

Solve the inequality $$-3x \u003e 15$$ and write the solution in set-builder notation.

Accepted Answer

$$\{x|x \u003c -5\}$$

Question 5

A gym charges a $$50$$ dollar membership fee plus $$20$$ dollars per month. Another gym charges $$35$$ dollars per month with no membership fee. For how many months will the first gym be cheaper? (Let $$m be $$the number of months.)

Accepted Answer

$$m \u003c 3.33$$

Question 6

Which of the following is the correct graph for the solution set $$x \u003e a$$?

Accepted Answer

A number line with an open circle at $$a$$ and shading to the right

Question 7

Solve the inequality $$3x - 8 \u003e x + 4$$ and write the solution in interval notation.

Accepted Answer

$$(6, \infty)$$

Question 8

Translate the sentence: 'You must score no less than 75 on the final' into an inequality.

Accepted Answer

$$x \geq 75$$

Question 9

Let $$f(x) = 2(3-x) + 5x$$ and $$g(x) = x + 7. $$For which values of $$x is$$ $$f(x) \leq g(x)$$?

Accepted Answer

$$x \leq 1$$

Question 10

Solve the inequality $$\frac{1}{2}x \geq -1$$ and write the solution in interval notation.

Accepted Answer

$$[-2, \infty)$$

Question 11

A moving company offers two rental plans: Plan A is $$99$$ with unlimited mileage, and Plan B is $$49$$ plus $$0.80$$ per mile. For what mileage $$m$$ does Plan A save money?

Accepted Answer

$$m \u003e 62.5$$

Question 12

Which of the following is the correct set-builder notation for the interval $$(-\infty, a]$$?

Accepted Answer

$$\{x|x \leq a\}$$

Question 13

Solve the inequality $$9x + 14 \u003e 7x + 10$$ and write the solution in set-builder notation.

Accepted Answer

$$\{x|x \u003e -2\}$$

Question 14

Which of the following is true when you multiply both sides of an inequality by a negative number?

Accepted Answer

The direction of the inequality reverses.

Question 15

Jonas was billed less than $$150$$ for copier repair at $$65$$ plus $$45$$ per hour. What is the maximum number of hours Jonas' copier could have been worked on?

Accepted Answer

$$1.88$$ hours$

Question 16

Which interval notation represents all real numbers less than $$a$$?

Accepted Answer

$$(-\infty, a)$$

Section 4.1: Inequalities and Applications – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard