Solving Equations and Inequalities

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

16. $b-3\le 15$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$5x<35$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

18. $\frac{d}{2}>-4$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

19. $-\frac{g}{3}\ge -9$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

20. $-8p\ge 24$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

22. $14>7y-21$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

23. $-27<8m+5$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

24. $6b+11\ge 15$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

 $2\left(4t+9\right)\le 18$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

26. $90\ge 5\left(2r+6\right)$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

27. $14-8n\le 0$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

28. $-4\left(5w-8\right)<33$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$0.02x+5.58<0$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

30. $1.5-0.25c<6$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$6d+3\ge 5d-2$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

32. $9z+2>4z+15$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

33. $2\left(g+4\right)<3g-2\left(g-5\right)$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$3\left(a+4\right)-2\left(3a+4\right)\le 4a-1$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

35. $y<\frac{-y+2}{9}$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$\frac{1-4p}{5}<0.2$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

37. $\frac{4x+2}{6}<\frac{2x+1}{3}$

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line. 

$12\left(\frac{1}{4}-\frac{n}{3}\right)\le -6n$

PART-TIME JOB

David earns $\backslash (5.60$ an hour working at Box Office Videos. Each week, $25\%$ of his total pay is deducted for taxes. If David wants his take-home pay to be at least $\backslash )105$ a week, solve the inequality $5.6x-0.25\left(5.6x\right)\ge 105$ to determine how many hours he must work. 

Juan’s parents gave him $\backslash (35$ to spend at the State Fair. He spends $\backslash )13.25$ for food. If rides at the fair cost $\$1.50$ each, solve the inequality $1.5n+13.25\le 35$ to determine how many rides he can afford.

Define a variable and write an inequality for each problem and then solve.

The sum of a number and 8 is more than 2.

Define a variable and write an inequality for each problem and then solve.

42. The product of a $-4$ and a number is at least 35.

Define a variable and write an inequality for each problem and then solve.

The difference of one half of a number and 7 is greater than or equal to 5.

Define a variable and write an inequality for each problem and then solve.

One more than product of $-3$ and a number is less than 16.

Define a variable and write an inequality for each problem and then solve.

45. Twice the sum of a number and 5 is no more than 3 times that same number increased by 11.

Define a variable and write an inequality for each problem and then solve.

9 less than a number is at most that same number divide by 2.

By Ohio law, when children are napping, the number of children per childcare staff member may be as many as twice the maximum listed at the right. Write and solve an inequality to determine how many staff members are required to be present in a room where 17 children are napping and the youngest child is 18 months old.

CAR SALES: For Exercise 48 and 49, use the following information.

Mrs. Lucas earns a salary of $\backslash (24,000$ per year plus $1.5\%$ commission on her sales. If the average price of a car she sells is $\backslash )30,500$, about how many cars must she sell to make an annual income of at least $\$40,000$.

48. Write an inequality to describe this situation.

CAR SALES: For Exercise 48 and 49, use the following information.

Mrs. Lucas earns a salary of $\backslash (24,000$ per year plus $1.5\%$ commission on her sales. If the average price of a car she sells is $\backslash )30,500$, about how many cars must she sell to make an annual income of at least $\$40,000$.

49. Solve the inequality and interpret the solution.

TEST GRADES: For Exercise 50 and 51, use the following information.

Ahmik’s scores on the first four of five 100-point history tests were 85, 91, 89 and 94.

50.  If a grade of at least 90 is A, write an inequality to find the score Ahmik must receive on the fifth test to have an A test average.

Ahmik’s scores on the first four of five 100-point history tests were 85, 91, 89 and 94. 

Solve the inequality and interpret the solution if he need to get at least an average of 90 with grade A.

Which of the following properties hold for inequalities? Explain your reasoning or give a counterexample.

Explain how inequalities can be used to compare phone plans.

1. Solve $2\text{d}+5=8\text{d}+2$. Check the solution.

2. Solve $\text{s}=\frac{1}{2}{\text{gt}}^2$ for g.

3. Evaluate $\left|\text{x}-3\text{y}\right|$ if $\text{x}=-8$ and $\text{y}=2$.

Solve $3\left|3\text{x}+2\right|=51$. Check the solution.

5.  Solve $2\left(\text{m}-5\right)-3\text{m}\left(2\text{m}-5\right)<5\text{m}+1$. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

If $4-5\text{n}\ge -1$, then $\text{n}$ could equal all of the following except:

A. $-\frac{1}{5}$                          B. $\frac{1}{5}$                      C. $1$                       D. $2$

If $\text{a}<\text{b}$ and $\text{c}<0$, state which of the following is true.

I. $\text{ac}>\text{bc}$                         II. $\text{a}+\text{c}<\text{b}+\text{c}$                    III. $\text{a}-\text{c}>\text{b}-\text{c}$

A. I only                                 B. II only                      C. III only                       

D. I and II only                      E. I, II, and III.

Use a graphing calculator to solve each inequality.

56. $\mathbf{-}\mathbf{5}\mathbf{x}\mathbf{-}\mathbf{8}\mathbf{<}\mathbf{7}$

Use a graphing calculator to solve each inequality.

$\mathbf{-}\mathbf{4}\left(\mathbf{6}\mathbf{x}\mathbf{-}\mathbf{3}\right)\le \mathbf{60}$

Use a graphing calculator to solve each inequality.

$\mathbf{3}\left(\mathbf{x}\mathbf{+}\mathbf{3}\right)\ge \mathbf{2}\left(\mathbf{x}\mathbf{+}\mathbf{4}\right)$

Solve each equation. Check the solution.

59.  If $\left|\text{x}-3\right|=17$

Solve each equation. Check the solution.

 If $8\left|4\text{x}-3\right|=64$