ATI TEAS Guide To Math | Algebraic Equations Question Review

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 = -4

Then, multiply both sides by -4 to isolate the variable x:
– x/4 = -4
– x/4 x (- x/4) = -4 x -4
X = 16

The value of x is 16.

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 = 3x²

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 3x² + 5x + 2.

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.

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

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.

To simplify this expression, combine like terms:

(2x² + 4x – 7) – (2x^x + 3x -4)

= 2x² – 2x² + 4x – 3x – 7 – (-4)

= (2x² – 2x²) + (4x – 3x) – (7 + 4)

= 0 + x – 3

= x – 3

The simplified expression is x – 3.

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

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}.