Question 1

Solve the inequality. $$| x | < 5$$

Accepted Answer

The inequality $| x | < 5$ means that the distance between $x$ and 0 on the number line is less than 5. This includes all real numbers between -5 and 5, but not including -5 and 5 themselves, hence the interval notation $( - 5,5 )$.

Question 2

Solve the equation. $$| x + 9 | > 7$$

Accepted Answer

The answer of Solve the equation. \[| x + 9...

Question 3

Solve the problem by setting up and solving an appropriate inequality. Sue bowled 150 and 140 in her first two games. What must she bowl in the third game to have an average of at least 170 for the three games?

Accepted Answer

To find the score Sue needs in her third game, set up the inequality: $(150 + 140 + x)/3 \geq 170$. Solving for $x$, we get $x \geq 220$.

Question 4

To hold the temperature of a room between $11 ^ { \circ } \mathrm { C }$ and $28 ^ { \circ } \mathrm { C }$ what Fahrenheit temperatures must be maintained?

Accepted Answer

To convert Celsius to Fahrenheit, use the formula $ F = \frac{9}{5}C + 32 $. For $11 ^{\circ}C$, $ F = \frac{9}{5}(11) + 32 = 51.8 ^{\circ}F $. For $28 ^{\circ}C$, $ F = \frac{9}{5}(28) + 32 = 82.4 ^{\circ}F $. Thus, the range is $51.8 ^{\circ} < F < 82.4 ^{\circ}$.

Question 5

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour. ACTION Truck Rental Big $22 \mathrm { ft }$ Truck Only \$26.95 for one hour. $\$ 7.95$ for each extra hour.

Accepted Answer

The answer of How long can a person rent the...

Question 6

Solve the equation, if possible. $$| x + 4 | = 12$$

Accepted Answer

The equation $| x + 4 | = 12$ can be solved by considering both the positive and negative scenarios of the absolute value. For the positive scenario, $x + 4 = 12$, which simplifies to $x = 8$. For the negative scenario, $-(x + 4) = 12$, which simplifies to $x = -16$. Therefore, the solutions are $x = 8$ and $x = -16$.

Question 7

Solve the equation, if possible. $$| 5 x + 7 | = - | 9 x - 2 |$$

Accepted Answer

The equation has no solution since the absolute value of any number is always either zero or positive, whereas the left-hand side is always non-negative while the right-hand side is always non-positive. Therefore, the two sides can never be equal for any value of $x$, and there is no solution.

Question 8

Solve the equation. $$| 3 x - 21 | + 15 = 21$$

Accepted Answer

The answer of Solve the equation. \[| 3 x -...

Question 9

Solve the equation. Give the solution in interval notation. $$| 4 - 5 x | \geq 14$$

Accepted Answer

To solve $| 4 - 5 x | \geq 14$, we consider two cases: $4 - 5x \geq 14$ and $4 - 5x \leq -14$. Solving the first gives $x \leq -2$, and solving the second gives $x \geq \frac{18}{5}$. Thus, the solution in interval notation is $( - \infty , - 2 ] \cup \left[ \frac { 18 } { 5 } , \infty \right)$.

Question 10

Solve the inequality. Use interval notation to describe the solution. $3 \leq - 7 x + 10 \leq 17$

Accepted Answer

To solve the inequality, we can start by subtracting 10 from all parts:

\begin{align*}
3 & \leq -7x + 10 \leq 17 \
-7 &\leq -7x \leq 7 \
-7/(-7) &\geq x \geq 7/(-7) \
1 &\geq x \geq -1 \
\end{align*}

So the solution is $-1\leq x\leq 1$, which in interval notation is $[-1,1]$. Thus the answer is choice C.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve the inequality. $| x | < 5$

Solve the equation. $| x + 9 | > 7$

Solve the problem by setting up and solving an appropriate inequality. Sue bowled 150 and 140 in her first two games. What must she bowl in the third game to have an average of at least 170 for the three games?

To hold the temperature of a room between $11 ^ { \circ } \mathrm { C }$ and $28 ^ { \circ } \mathrm { C }$ what Fahrenheit temperatures must be maintained?

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour. ACTION Truck Rental Big $22 \mathrm { ft }$ Truck Only \$26.95 for one hour. $\$ 7.95$ for each extra hour.

Solve the equation, if possible. $| x + 4 | = 12$

Solve the equation, if possible. $| 5 x + 7 | = - | 9 x - 2 |$

Solve the equation. $| 3 x - 21 | + 15 = 21$

Solve the equation. Give the solution in interval notation. $| 4 - 5 x | \geq 14$

Solve the inequality. Use interval notation to describe the solution. $3 \leq - 7 x + 10 \leq 17$

Quiz 2: Equations, Inequalities, and Problem Solving

Solve the inequality. ∣x∣<5| x | < 5∣x∣<5

Solve the equation. ∣x+9∣>7| x + 9 | > 7∣x+9∣>7

Solve the problem by setting up and solving an appropriate inequality. Sue bowled 150 and 140 in her first two games. What must she bowl in the third game to have an average of at least 170 for the three games?

To hold the temperature of a room between 11∘C11 ^ { \circ } \mathrm { C }11∘C and 28∘C28 ^ { \circ } \mathrm { C }28∘C what Fahrenheit temperatures must be maintained?

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour. ACTION Truck Rental Big 22ft22 \mathrm { ft }22ft Truck Only \$26.95 for one hour. $7.95\$ 7.95$7.95 for each extra hour.

Solve the equation, if possible. ∣x+4∣=12| x + 4 | = 12∣x+4∣=12

Solve the equation, if possible. ∣5x+7∣=−∣9x−2∣| 5 x + 7 | = - | 9 x - 2 |∣5x+7∣=−∣9x−2∣

Solve the equation. ∣3x−21∣+15=21| 3 x - 21 | + 15 = 21∣3x−21∣+15=21

Solve the equation. Give the solution in interval notation. ∣4−5x∣≥14| 4 - 5 x | \geq 14∣4−5x∣≥14

Solve the inequality. Use interval notation to describe the solution. 3≤−7x+10≤173 \leq - 7 x + 10 \leq 173≤−7x+10≤17

Solve the inequality. $| x | < 5$

Solve the equation. $| x + 9 | > 7$

To hold the temperature of a room between $11 ^ { \circ } \mathrm { C }$ and $28 ^ { \circ } \mathrm { C }$ what Fahrenheit temperatures must be maintained?

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour. ACTION Truck Rental Big $22 \mathrm { ft }$ Truck Only \$26.95 for one hour. $\$ 7.95$ for each extra hour.

Solve the equation, if possible. $| x + 4 | = 12$

Solve the equation, if possible. $| 5 x + 7 | = - | 9 x - 2 |$

Solve the equation. $| 3 x - 21 | + 15 = 21$

Solve the equation. Give the solution in interval notation. $| 4 - 5 x | \geq 14$

Solve the inequality. Use interval notation to describe the solution. $3 \leq - 7 x + 10 \leq 17$