Math / Algebra

QuestionTwo of the most expensive cars in the world are car $A$ and car $B$ . The prices of these two cars differ by more than $\$ 10,000$ . The price of car $A$ is $\$ 130,745$ . a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the price of car B . b. What are the possibilities for the price of car $B$ ? a. Write an absolute value inequality that describes the given situation. $\square$ (Do not include the $\$$ symbol in your answer.) Help me solve this View an example Get more help a Clear al 16

Studdy Solution

STEP 1

1. The price of car $A$ is given as $130,745$ dollars.
2. We need to express the condition that the price of car $B$ , denoted by $x$ , differs by more than $10,000$ dollars compared to the price of car $A$ .
3. The inequality involves the absolute value to account for the possibility that car $B$ could be either more expensive or less expensive than car $A$ .

STEP 2

1. Formulate the absolute value inequality.
2. Solve the absolute value inequality to find the range of possible prices for car $B$ .

STEP 3

Form the absolute value inequality that represents the condition that the price of car $B$ differs by more than $10,000$ dollars from the price of car $A$ .
$|x - 130745| > 10000$

STEP 4

To solve the absolute value inequality $|x - 130745| > 10000$ , we need to consider the definition of absolute value and split it into two separate inequalities:
$x - 130745 > 10000 \quad \text{or} \quad x - 130745 < -10000$

STEP 5

Solve the first inequality $x - 130745 > 10000$ :
$x > 130745 + 10000$
$x > 140745$

STEP 6

Solve the second inequality $x - 130745 < -10000$ :
$x < 130745 - 10000$
$x < 120745$

STEP 7

Combine the solutions from the two inequalities to express the complete solution for the price of car $B$ :
$x < 120745 \quad \text{or} \quad x > 140745$
Solution: The absolute value inequality that describes the given situation is:
$|x - 130745| > 10000$
The possibilities for the price of car $B$ are:
$x < 120745 \quad \text{or} \quad x > 140745$

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Formulate the absolute value inequality.
2. Solve the absolute value inequality to find the range of possible prices for car $B$ .

STEP 3

Form the absolute value inequality that represents the condition that the price of car $B$ differs by more than $10,000$ dollars from the price of car $A$ .
$|x - 130745| > 10000$

STEP 4

To solve the absolute value inequality $|x - 130745| > 10000$ , we need to consider the definition of absolute value and split it into two separate inequalities:
$x - 130745 > 10000 \quad \text{or} \quad x - 130745 < -10000$

STEP 5

Solve the first inequality $x - 130745 > 10000$ :
$x > 130745 + 10000$
$x > 140745$

STEP 6

Solve the second inequality $x - 130745 < -10000$ :
$x < 130745 - 10000$
$x < 120745$

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Formulate the absolute value inequality.2. Solve the absolute value inequality to find the range of possible prices for car BBB.

STEP 3

Form the absolute value inequality that represents the condition that the price of car BBB differs by more than 10,00010,00010,000 dollars from the price of car AAA. ∣x−130745∣>10000 |x - 130745| > 10000 ∣x−130745∣>10000

STEP 4

STEP 5

Solve the first inequality x−130745>10000x - 130745 > 10000x−130745>10000:x>130745+10000 x > 130745 + 10000 x>130745+10000x>140745 x > 140745 x>140745

STEP 6

Solve the second inequality x−130745<−10000x - 130745 < -10000x−130745<−10000:x<130745−10000 x < 130745 - 10000 x<130745−10000x<120745 x < 120745 x<120745

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Formulate the absolute value inequality.
2. Solve the absolute value inequality to find the range of possible prices for car $B$ .

Form the absolute value inequality that represents the condition that the price of car $B$ differs by more than $10,000$ dollars from the price of car $A$ .
$|x - 130745| > 10000$

Solve the first inequality $x - 130745 > 10000$ :
$x > 130745 + 10000$
$x > 140745$

Solve the second inequality $x - 130745 < -10000$ :
$x < 130745 - 10000$
$x < 120745$