ATI TEAS Guide To Math  Algebraic Equations Question Review
ATI TEAS Math Algebra
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Question 1 of 8
1. Question
12 – x/4 = 8
Solve the equation above. Which of the following is correct?
Correct
Isolate the variable x on one side of the equation. First, subtract the number 12 from both sides:
12 – x/4 = 8
– x/4 = 8 – 12
– x/4 = 4Then, multiply both sides by 4 to isolate the variable x:
– x/4 = 4
– x/4 x ( x/4) = 4 x 4
X = 16The value of x is 16.
Incorrect
Isolate the variable x on one side of the equation. First, subtract the number 12 from both sides:
12 – x/4 = 8
– x/4 = 8 – 12
– x/4 = 4Then, multiply both sides by 4 to isolate the variable x:
– x/4 = 4
– x/4 x ( x/4) = 4 x 4
X = 16The value of x is 16.

Question 2 of 8
2. Question
(3x + 2)(x + 1)
Simplify the expression above. Which of the following is correct?
Correct
Use the process of FOIL to multiply the binomials (3x + 2)(x + 1). First, multiply the first two terms of each binomial:
First: 3x x x = 3x^{2}
Then, multiply the outer two terms:
Outer: 3x x 1 = 3x
Then, multiply the inner two terms:
Inner: 2 x x = 2x
Then multiply the last two terms:
Last: 2 x 1 = 2
This expression can be further simplified to 3x^{2} + 5x + 2.
Incorrect
Use the process of FOIL to multiply the binomials (3x + 2)(x + 1). First, multiply the first two terms of each binomial:
First: 3x x x = 3x^{2}
Then, multiply the outer two terms:
Outer: 3x x 1 = 3x
Then, multiply the inner two terms:
Inner: 2 x x = 2x
Then multiply the last two terms:
Last: 2 x 1 = 2
This expression can be further simplified to 3x^{2} + 5x + 2.

Question 3 of 8
3. Question
x + 2 > 4
Solve the inequality above. Which of the following is correct?
Correct
In this inequality, the absolute value of x + 2 is greater than 4. This tells us that the quantity x + 2 lies more than 4 units away from zero on the number line. So, the value of x + 2 could be greater than 4, or it could be less than 4. Set up two inequalities and solve for both possibilities:
X + 2 > 4 x + 2 < 4
X + 2 2 > 4 – 2 x + 2 – 2 < 4 – 2
X > 2 x < 6
The solution is x > 2 or x < 6.
Incorrect
In this inequality, the absolute value of x + 2 is greater than 4. This tells us that the quantity x + 2 lies more than 4 units away from zero on the number line. So, the value of x + 2 could be greater than 4, or it could be less than 4. Set up two inequalities and solve for both possibilities:
X + 2 > 4 x + 2 < 4
X + 2 2 > 4 – 2 x + 2 – 2 < 4 – 2
X > 2 x < 6
The solution is x > 2 or x < 6.

Question 4 of 8
4. Question
Cassandra’s height, x, is 3 inches greater than twice her brother’s height, y.
Which of the following algebraic equations best represents the statement above?
Correct
Start with Cassandra’s height, x. Then set up an equation:
X = ?
Cassandra’s brother’s height is denoted by y. Cassandra’s height is equal to 3 more than twice y, which can be written as 2y + 3. Add this expression to the equation:
X = 2y + 3
Incorrect
Start with Cassandra’s height, x. Then set up an equation:
X = ?
Cassandra’s brother’s height is denoted by y. Cassandra’s height is equal to 3 more than twice y, which can be written as 2y + 3. Add this expression to the equation:
X = 2y + 3

Question 5 of 8
5. Question
4(x +7) = 2(x + 15)
Solving the equation above. Which of the following is correct?
Correct
Isolate the variable x on one side of the equation.
First, perform the multiplication on both sides of the equation:
4(x + 7) = 2(x + 15)
4x + 28 = 2x + 30
Then, subtract 28 from both sides:
4x + 28 = 2x + 30
4x + 28 – 28 = 2x + 30 – 28
4x = 2x + 2
Next, subtract 2x from both sides:
4x = 2x + 2
4x – 2x = 2
2x = 2
Now, divide both sides by 2 to isolate the variable x:
2x = 2
2x / 2 = 2 / 2
X = 1
The value of x is 1.
Incorrect
Isolate the variable x on one side of the equation.
First, perform the multiplication on both sides of the equation:
4(x + 7) = 2(x + 15)
4x + 28 = 2x + 30
Then, subtract 28 from both sides:
4x + 28 = 2x + 30
4x + 28 – 28 = 2x + 30 – 28
4x = 2x + 2
Next, subtract 2x from both sides:
4x = 2x + 2
4x – 2x = 2
2x = 2
Now, divide both sides by 2 to isolate the variable x:
2x = 2
2x / 2 = 2 / 2
X = 1
The value of x is 1.

Question 6 of 8
6. Question
(2x^{2} + 4x 7) – (2x^{2} + 3x 4)
Simplify the expression above. Which of the following is correct?
Correct
To simplify this expression, combine like terms:
(2x^{2} + 4x – 7) – (2x^{x} + 3x 4)
= 2x^{2} – 2x^{2} + 4x – 3x – 7 – (4)
= (2x^{2} – 2x^{2}) + (4x – 3x) – (7 + 4)
= 0 + x – 3
= x – 3
The simplified expression is x – 3.
Incorrect
To simplify this expression, combine like terms:
(2x^{2} + 4x – 7) – (2x^{x} + 3x 4)
= 2x^{2} – 2x^{2} + 4x – 3x – 7 – (4)
= (2x^{2} – 2x^{2}) + (4x – 3x) – (7 + 4)
= 0 + x – 3
= x – 3
The simplified expression is x – 3.

Question 7 of 8
7. Question
The value of x is less than 3/4 the value of y.
Which of the following algebraic expressions correctly represents the sentence above?
Correct
Start with the value if x, and set up an equation:
X = ?
The question tells us that x is 5 less than 3/4 the value of y, which can be written as 3/4 y – 5. Add this expression into the equation:
X =3/4 y – 5
Incorrect
Start with the value if x, and set up an equation:
X = ?
The question tells us that x is 5 less than 3/4 the value of y, which can be written as 3/4 y – 5. Add this expression into the equation:
X =3/4 y – 5

Question 8 of 8
8. Question
9 – x = 4
Which of the following is the solution set for the equation above?
Correct
In this equation, the absolute value of 9 – x is 4. This tells us that the quantity 9 – x lies exactly 4 units away from zero on the number line. So, 9 – x could equal 4 or 4. Set up two equations and solve for both possibilities:
9 – x = 4 9 – x = 4
9 – 9 – x = 4 – 9 9 – 9 – x = 4 – 9
x = 5 x = 13
x = 5 x = 13
The value of x is 5 or 13. In set notation, this is written as {5, 13}.
Incorrect
In this equation, the absolute value of 9 – x is 4. This tells us that the quantity 9 – x lies exactly 4 units away from zero on the number line. So, 9 – x could equal 4 or 4. Set up two equations and solve for both possibilities:
9 – x = 4 9 – x = 4
9 – 9 – x = 4 – 9 9 – 9 – x = 4 – 9
x = 5 x = 13
x = 5 x = 13
The value of x is 5 or 13. In set notation, this is written as {5, 13}.