Which of the following is the value of x in the equation below? (left|3x-7 ight|-13=2)
A. x = 21/3, x=22/3
B. x = 7/3, x=9/3
C. x = 15/2, x=9/3
D. x = 22/3, x=-8/3
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Add 13 to both sides to isolate the absolute value term, resulting in ( left|3x-7 ight|= 15)
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Consider two cases:
- When (+(3x-7)) is positive, solve for x to get (3x = 15 + 7) then (3x=22) (finally x=frac{22}{3})
- When (-(3x-7)) is negative (but the absolute value makes it positive). Solve for x to get (-3x = 15 - 7) then (-3x=8) (finally x=- frac{8}{3})
So, there are two possible solutions: (x=frac{22}{3} or x=- frac{8}{3})
Therefore, the Correct Answer is D.
More Questions on TEAS 7 Math
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Q #1: Which of the following is the length of the unknown leg of a right triangle that has one leg length of 6 feet and a hypotenuse of 14 feet? (Round to the nearest tenth.)
A. 15 feet
B. 12.6 feet
C. 18.3 feet
D. 9.2 feet
Answer Explanation
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Q #2: A plastic bucket containing 4/5 gallons of water is 3/4 full. How many gallons of water is in one fully filled bucket?
A. 1 1/15
B. 2 4/15
C. 9/15
D. 11/15
Answer Explanation
Given:
- A plastic bucket containing 4/5 gallons of water is 3/4 full.
To find:
- How many gallons of water is in one fully filled bucket?
Let's use the proportion formula to solve this:
If 3/4 of the bucket is 4/5 gallons, then 1 full bucket (or 4/4 of the bucket) will contain how many gallons?
\(\frac{3}{4}\) of the bucket = \(\frac{4}{5}\) gallons \(\frac{4}{3}\) of the bucket = \(\frac{5}{4}\) gallons \(\frac{4}{4}\) of the bucket=\(?\) gallons
\(\frac{4}{4}\) of the bucket = x gallons
Cross multiplying: x = \(\frac{4}{4}*\frac{4}{5}\ *\ \frac{4}{3}x = \frac{4}{5}*\frac{4}{3} = x\)
\(x\ =\ \frac{16}{15}\)
Thus, a fully filled bucket contains \(\frac{16}{15}\ =\ 1\frac{1}{15}\) gallons of water. Therefore, the correct choice is:
Choice A: 1 1/15
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Q #3: (frac{[2 (8 + 2 * 6)]}{(16 div 2)} = frac{40}{8} = 5) Simplify the expression above. Which of the following is correct?
A. 6
B. 2
C. 5
D. 3
Answer Explanation
We follow the order of operations to solve the given expression.
First, we start with the numerator and solve
[2(8+2*6)]
We start with multiplication in inner brackets, 2*6=12. The expression becomes
[2(8+12)]
Then, we conduct the addition of 8+12=20. Then, the expression yields
[2(20)] = 2*20 = 40
Now, we solve for denominator, which is 16/2=8.
Thus, the expression is reduced into
(frac{[2 (8 + 2 * 6)]}{(16 div 2)} = frac{40}{8} = 5)
The expression reduces into 5.
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Q #4: A macaroni and cheese recipe calls for 4/7 cup of flour for every 2 1/5 cup of milk. To make a bigger batch, the chef uses 4 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
A. 15 1/5 cups
B. 15 2/5
C. 12 8/15 cups
D. 15 cups
Answer Explanation
To find the required number of cups of milk, we need to set up a proportion equation. If we let x be the required number of cups and cups of flour as numerator and cups of milk in denominator, then the result proportion becomes:
We cannot multiply mixed fractions with any number, so we change 2 1/5 into an improper fraction as
The proportion equation becomes
Cross-multiply to solve for x
As a mixed fraction, 77/5 becomes 15 2/5. Therefore, to make a bigger batch, the chef needs 15 2/5 cups of milk.
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Q #5: Three friends are sharing a pizza. One friend eats three-quarters of the pizza. The other two friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
A. 1/6
B. 3/4
C. 2/3
D. 1/5
Answer Explanation
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Q #6: A motor company’s stock price was $33.20 on Tuesday. On Wednesday, the price went up $2.45. On Thursday, the price decreased from Wednesday’s price by $1.50. On Friday, the price went up $1.62 from Thursday’s price. Which of the following was the final price on Friday?
A. $35.65
B. $34.15
C. $35.77
D. $34.82
Answer Explanation
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Q #7: A bag contains three green balls, four red balls, and six yellow balls. If one ball is randomly selected from the ball, which of the following is the probability that the ball is yellow?
A. 10/13
B. 4/13
C. 3/13
D. 6/13
Answer Explanation
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Q #8: Which of the following is the value of x in the equation below? (left|3x-7 ight|-13=2)
A. x = 21/3, x=22/3
B. x = 7/3, x=9/3
C. x = 15/2, x=9/3
D. x = 22/3, x=-8/3
Answer Explanation
-
Add 13 to both sides to isolate the absolute value term, resulting in ( left|3x-7 ight|= 15)
-
Consider two cases:
- When (+(3x-7)) is positive, solve for x to get (3x = 15 + 7) then (3x=22) (finally x=frac{22}{3})
- When (-(3x-7)) is negative (but the absolute value makes it positive). Solve for x to get (-3x = 15 - 7) then (-3x=8) (finally x=- frac{8}{3})
So, there are two possible solutions: (x=frac{22}{3} or x=- frac{8}{3})
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Q #9: The length of a rectangular room is 2 feet greater than its width. Which of the following equations represents the area (A) of the room?
A. A=x(x+2)
B. A=2x+2(x+2)
C. A=2x(x+2)
D. A=2x
Answer Explanation
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Q #10: ((frac{x}{y}) + rw = z) Solve for x in the equation above.
A. x=y(z-rw)
B. x=rw(y-z)
C. x=w(z+ry)
D. x=rwy-z
Answer Explanation
The question requires us we make x the subject of the formula.
First, we subtract rw to both sides of the equation
Multiply both sides by y
Thus, the formula for finding the value of x is y(z-rw).
