Which of the following is the value of x in the equation below

A. x= -1/2 or x=3/2

B. x= -1 or x=2

C. x =-2 or x= 1

D. x= -3/2 or x= 1/2

Answer Explanation:

We need to find the value of x from the given equation. First, we move the value of 10 to the right-hand side of the equation.

Add 10 to both sides of the equation

Next, we apply the absolute rule:

, a>0, then u=a or u=-a

In this case a=12, which is greater 0. Then, the first condition becomes

Solving for x

The second condition becomes

Solving for x

Then, the value of x is -1 or 2.

Therefore, the Correct Answer is B.

Q #1: A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cup of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?

A. 7 1/5 cups

B. 2 2/5 cups

C. 3 8/15 cups

D. 6 cups

Answer Explanation

We are being asked to find the amount of milk needed. This is a proportion problem, which compares the amount of flour to that of milk. Letting x represent the amount of milk required, we set up the proportion with flour on the numerator and amount of milk in denominator as follows:

Change the mixed fraction of 1 1/5 into improper fraction as follows

The proportion equation becomes

Cross-multiply to solve for x

As an mixed fraction, 36/5 becomes 7 1/5. Therefore, 7 1/5 cups of milk are needed to make a big batch of 2 cups.
Q #2: Which of the following is the best estimate of the number of centimeters (cm) in 1 yard? (Note: 1 yard=3 feet; 1 foot =12 inches; 1 inch =2.54 cm)

A. 72 cm

B. 180 cm

C. 36 cm

D. 90 cm

Answer Explanation

We convert the given value in yard to the cm using the following set up.

The value 91.44 cm is close to 90 cm. Therefore, 1 yard is approximately 90 cm.
Q #3: Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?

A. 1/6

B. 1/3

C. ¼

D. 1/5

Answer Explanation

What fraction of the pizza the other three friends get is what is asked to find.

First, the pizza is whole, representing a value of 1. Then, one friend ate half of the pizza. Thun, the fraction of the pizza the friend gets is:

First friend eats =1/2 of 1=1/2

Remaining fraction of the pizza=1-1/2=1/2

Now, the three friends share ½ amongst themselves equally. Then, each friend gets

The three friends each gets 1/6 of the pizza.