Which of the following is the value of x in the equation below? 4x- 3- 5x=24
A. -27
B. -6
C. 3
D. 21
to solve for x, we order like terms together and proceed as follows:
4x-3-5x=24
Add 3 to both sides of the equation
4x-3+3-5x=24+3
4x+3-3-5x=27
4x-5x=27
-x=27
Divide both sides by -1
-x/-1=27/-1
x= -27
Thus, the unknown value of x is -27
Therefore, the Correct Answer is A.
More Questions on TEAS 7 Math
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Q #1: Which of the following values is the greatest?
A. 9/2
B. 10/3
C. 4.4
D. 4.25
Answer Explanation
We are given a mix of fractions and decimals and to compare the numbers, we convert the given decimals to fractions.
4.4 becomes 44/10
4.25 becomes 425/100
Now the set of fractions for comparison are: 9/2, 10/3, 44/10, and 425/100. The least common denominator for 2, 3 and 10 is 300. Then,
9/2*300=1350
10/3*300=1000
44/10*300=1320
425/10*300=1275
From the above products, 9/2 gives the greatest value when the fractions are compared with the least common denominator of the given denominators.
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Q #2: The width of a rectangle is 4 inches (in) and the area of the rectangle is 32 in2. Which of the following is the length of the rectangle?
A. 8 in
B. 28 in
C. 36 in
D. 128 in
Answer Explanation
We need to find the length of the rectangle from the given area and width of the rectangle. Let L be length if the rectangle. Then,
Area of rectangle=Length*width
Substituting area=32 in2 and w=4 inches
32=L*4
32=4L
Divide both sides by 4
32/4=4L/4
8=L
The length of the rectangle is 8 inches.
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Q #3: Simplify the expression below. Which of the following is correct? \(18x^5yz\ \div\ \ 6xyz^4\)
A. \(3x^4z^3\)
B. \(3x^4yz^3\)
C. \(\frac{(3x)^4}{z^3}\)
D. \(\frac{(3x^4)}{z^3}\)
Answer Explanation
We use the properties of exponent with the same base to solve for above expression.
Multiplication of exponents with same base, we add the exponents
Division of exponents with same base, we subtract the exponents
Using these two properties, we can solve the expression:
Now we use the following properties:
y0 =1, and
, thus
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Q #4: A local law school reports that 74% of last year's graduates are employed by law firms, 3% work for the government and 2% work for nonprofit organizations. The rest of the graduates work at jobs unrelated to law. Based on these outcomes, which of the following is the percentage of graduates working jobs unrelated to law?
A. 5%
B. 79%
C. 69%
D. 21%
Answer Explanation
Percentages always add up to 100%. If we let x be the percent of graduates working for jobs unrelated to law, then
74%+3%+2%+x=100%
79%+x=100%
Subtract 79% from both sides of the equation
79%-79%+x=100%
x=100%-79%
x=21%
So, the number of graduates working for jobs unrelated to law is 21%.
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Q #5: The graph below compares the age of car to its value. Which of the following is the age of the car when its value is $12,500?
A. Between 2 and 3 years
B. Less than 1 year
C. Greater than 3 years
D. Between 1 and 2 years
Answer Explanation
We extrapolate the values of a line between 10 and 15 on y-axis to meet the curve and drop another line from the intersection of the curve to meet the x-axis and read off the age of the car.
Now, let’s extrapolate in the following diagram
The intersection of the line and the x-axis is between 4 and 5 years. This means that the car is about 4.5 years old. From the options given, the age of the car is more than 3 years old.
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Q #6: An athlete can run 6 miles in 51 minutes. At this rate, how many miles could the athlete run in 90 minutes?
A. 15 miles
B. 11.5 miles
C. 45 miles
D. 10.6 miles
Answer Explanation
Here, the athlete runs 6 miles in 51 minutes, which can be expressed as:
Now, in 90 minutes, the athlete will cover about
Therefore, the athlete runs about 10.6 miles in 90 minutes.
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Q #7: A family is planning a driving vacation and is estimating the price of gasoline. While on the vacation, the family plans to drive 3,000 miles. The car gets about 25 miles per gallon, and the cost of gasoline is $1.66 per gallon. Which of the following is the estimate for cost of gasoline for the vacation?
A. $120.00
B. $41.50
C. $72.29
D. $199.20
Answer Explanation
We solve the problem by first finding the amount of gallons needed for the whole trip then find the cost of the gallon.
The car uses 1 gallon to cover 25 miles, which is same as:
Now, in 3000 miles, the car will use how many gallons of gasoline?
A trip of 3000 miles will need 120 gallons. And to find the cost of 120 gallons, we proceed as follows:
The family will spend $199.20 to drive for 3000 miles.
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Q #8: A teacher has asked all the students in the class which days of the week they get up after 8 a.m. Which of the following is the best way to display the frequency for each day of the week?
A. Pie graph
B. Bar graph
C. Histogram
D. Scatterplot
Answer Explanation
The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.
Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week. Histograms are useful for understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.
As you can see below, the Histogram is used to depict a pattern/continuous data. While a bar graph does just fine even with discrete data.
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Q #9: For a school's annual budget, the total amount of money spent on supplies (s) and textbooks (t) cannot exceed $12,000. Which of the following inequalities represents this scenario?
A. s + t >= $12,000
B. s + t > $12,000
C. s + t < $12,000
D. s + t <= $12,000
Answer Explanation
We can interpret ‘cannot exceed” as less than ‘<’. Therefore, in our inequality, the symbol < must be included. Now let’s convert the word problem into a mathematical inequality.
Money spent on supplies=s
Money spent on textbooks=t
Total money spent=money spent on supplies + money spent on textbooks
Total money spent = s+t
But the money spent cannot exceed $12,000. Then,
s+t < $12,000.
However the money spent can still be equal to $12000, as it has not exceeded it.Therefore, the required inequality is s + t <= $12,000.
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Q #10: A patient drives 19 miles one way to a medical facility for treatment. How far does the patient drive round-trip in 22 days of treatment?
A. 1,254 miles
B. 1,672 miles
C. 418 miles
D. 836 miles
Answer Explanation
Round trip means to and from, which is twice the distance from home to a medical facility.
In one day, the round trip=19+19=38 miles
So, in 22 days, the round trip=38*22=836 miles.
The patient will cover 836 miles in 22 days.
