Solving Equations and Inequalities

Solve each equation. Check the solution.

61.  If $\left|\text{x}+1\right|=\text{x}$

On average, by how much did the number of people who just borrow, but not necessarily buy, online increase each year from 1997 to 2003?

Define a variable, write an equation, and solve the problem.

Name the sets of numbers to which each number belongs.

63. $31$

Name the sets of numbers to which each number belongs.

$-4.\overline{2}$

Name the sets of numbers to which each number belongs.

65. $\sqrt{7}$

Jenny baby-sat for $\mathbf{5}\frac{\mathbf{1}}{\mathbf{2}}$ hours on Friday night and 8 hours on Saturday. She charges $$\mathbf{4}\mathbf{.}\mathbf{25}$ per hour. Use the Distributive property to write two equivalent expressions that represent how much money Jenny earned.

Solve each equation. Check the solution.

$\left|\text{x}\right|=7$

Solve each equation. Check the solution.

68. $\left|\text{x}+5\right|=18$

Solve each equation. Check the solution.

$\left|5\text{y}-8\right|=12$

Solve each equation. Check the solution.

70. $\left|2\text{x}-36\right|=14$

Solve each equation. Check the solution.

$2\left|\text{w}+6\right|=10$

Solve each equation. Check the solution.

$\left|\text{x}+4\right|+3=17$

Write a compound inequality to describe the following situation.

Buy a present that costs at least \(5 and at most \)15.

 OPEN-ENDED: Write a compound inequality whose graph is the empty set.

FIND THE ERROR

Sabrina and Isaac are solving $|3x+7|>2$

Who is correct? Explain your reasoning.

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers are between -8 and 8.

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers greater than 3 and less than -3.

Write an absolute value inequality for each graph

6. 

Write an absolute value inequality.

Solve each inequality. Graph the solution set on a number line. 

$y-3>1or y+2<1$

Solve each inequality. Graph the solution set on a number line. 

$3<d+5<8$.

Solve each inequality. Graph the solution set on a number line. 

$\left|a\right|\ge 5$.

Solve each inequality. Graph the solution set on a number line. 

$\left|g+4\right|\le 9$.

Solve each inequality. Graph the solution set on a number line. 

$\left|4k-8\right|<20$.

Solve each inequality. Graph the solution set on a number line. 

$\left|w\right|\ge -2$.

FLOORING

Deion estimates that he will need between 55 and 60 ceramic tiles to retile his kitchen floor. If each tile costs $\$6.25,$ write and solve a compound inequality to determine what the cost $c$ of the tile could be.

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers greater than or equal to 5 or less than or equal to $-5$

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers less than 7 and greater than $-7$

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers between $-4$ and 4

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

18. all numbers less than or equal to  $-6$ or greater than or equal to 6 

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

 all numbers greater than 8 or less than $-8$ 

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

20. all numbers less than or equal to  $1.2$ and greater than or equal to  $-1.2$

Write an absolute value inequality for each graph

Write an absolute value inequality for each graph

Write an absolute value inequality for each graph

23. 

Write an absolute value inequality for each graph

Write an absolute value inequality for each graph

 Write an absolute value inequality for each graph

26. 

Solve each inequality. Graph the solution set on number line. 

$3p+1\le 7\text{ or }2p-9\ge 7$

Solve each inequality. Graph the solution set on number line. 

28. $9<3t+6<15$

Solve each inequality. Graph the solution set on number line. 

$-11<-4x+5<13$$-11<-4x+5<13$

Solve each inequality. Graph the solution set on number line. 

$2c-1<-5\text{ or }3c+2\ge 5$

Solve each inequality. Graph the solution set on number line. 

31. $-4<4f+24<4$

Solve each inequality. 

$a+2>-2\text{ or }a-8<1$

Solve each inequality. Graph the solution set on a number line.

33. $\left|g\right|\le 9$

Solve each inequality. Graph the solution set on a number line.

 $\left|2m\right|\ge 8$

Solve each inequality. Graph the solution set on a number line.

$\left|3k\right|<0$

Solve each inequality. Graph the solution set on a number line.

36. $\left|-5y\right|<35$

Solve each inequality. Graph the solution set on a number line.

$\left|b-4\right|>6$

Solve each inequality. Graph the solution set on a number line.

38. $\left|6r-3\right|<21$