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: A child has a bottle full of pennies, nickels, dimes, and quarters. There are three as many quarters as pennies, five times as many as nickels as pennies, and two times as many dimes as nickels. How many more dimes does the child have than nickels?
A. 4 times as many
B. 5 times as many
C. 2 times as many
D. 10 times as many
Answer Explanation
In this question, we need to find the ratio of dimes to quarters.
If we let x be number of pennies in the bottle. Then,
Number of quarters in the bottle = 3x
Number of nickels in the bottle = 5x
Number of dimes in the bottle =2(5x)=10x
Now relating dimes to quarters, we have
Thus, there are 2 times as many dimes as nickels in the box.
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Q #2: A pharmaceutical company’s stock price was $20.33 on Monday. On Tuesday, the price went up $0.35. On Wednesday, the price decreased from Tuesday’s price by $1.05. On Thursday, the price went up $0.95 from Wednesday’s price. Which of the following was the final price on Thursday?
A. $20.68
B. $19.63
C. $20.63
D. $20.58
Answer Explanation
Thursday’s stock price is found by determining the price of the stock on Tuesday and Wednesday.
Stock price on Monday= $20.33
Stock price on Tuesday= $(20.33+0.35)=$20.68
Stock price on Wednesday =$(20.68-1.05)=$19.63
Stock price on Thursday = $(19.63+0.95)=$20.58
Therefore, the price of the stock on Thursday was $20.58
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Q #3: There are 900 students enrolled in four allied health programs at a local community college. The percent students in each program are displayed in the pie chart. Which of the following is the number of students enrolled in the respiratory care program?
A. 162
B. 171
C. 378
D. 189
Answer Explanation
we use the percentages and number of students to find the number of students enrolled in the respiratory care program as in the pie chart. The total percent of the whole piec chart sums to 100%.
If we let x represent the number of students enrolled in the respiratory care program, we can set a proportion equation with number of students on the numerator and percentages on the denominator.
Find the value of x by cross-products
Divide both sides of the equation by 100%
Thus, 171 students out of 900 students will enroll for a respiratory care program.
