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Algebra II : Solving Expressions

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Example Question #1 : Solving Expressions

Solve for x.

3x(8)-5=-2(3x+5)

Possible Answers:

-1/6

1/6

-5/18

Correct answer:

-1/6

Explanation:

a. Simplify each side of the equation using the distributive property.

24x-5=-6x-10

b. Add 6x to both sides of the equation to move all terms with "x" to the left side of the equation.

30x-5=-10

c. Add 5 to both sides of the equation to move all constants to the right side of the equation.

30x=-5

d. Divide both sides of the equation by 30 to isolate the variable. Simplify the resulting fraction

x=-5/30=-1/6

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Example Question #2 : Solving Expressions

If x=4 , simplify $x^{2}+3x-4$ .

Possible Answers:

Correct answer:

Explanation:

First, you substitute for : $(4^{2})+3(4)-4$

Next, use PEMDAS (Parentheses, Exponents, Multiplication, Dividion, Addition, and Subtraction) to preform the algebraic operations in the correct order. When we apply this rule to simplify we get the following:

16+12-4

28-4

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Example Question #3 : Solving Expressions

Solve for if z=2 . $3z+y^{2}=22$ .

Possible Answers:

$\pm 4$

$\pm 8$

Correct answer:

$\pm 4$

Explanation:

First, substitute 2 for z: $3(2)+y^{2}=22$ .

Then, simplify: $6+y^{2}=22$ .

Next, you must isolate y by moving all other numbers and variables to the other side of the equation: $6+y^{2}-6=22-6$ , which gives you $y^{2}=22-6$ .

And simplify: $y^{2}=16$ .

Here, we then take the square root of both sides: $\sqrt{y^{2}}=\sqrt{16}$ .

Simplfy: $y=\pm 4$ , because both $-4\cdot-4=16$ and $4\cdot4=16$ .

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Example Question #4 : Solving Expressions

Simplify $z^{3}+x^{4}y^{2}-y^{3}+13$ given z=1, x=2, and y=3 .

Possible Answers:

131

149

Correct answer:

131

Explanation:

First, substitute 1 for z, 2 for x and 3 for y: $1^{3}+2^{4}3^{2}-3^{3}+13$ and simplify: $1+16\cdot9-27+13$ .

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we simplify the multiplication: 1+144-27+13 .

Then add and subtract from left to right: 145-27+13=118+13=131 .

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Example Question #5 : Solving Expressions

Emily buys a rose plant when it is inches tall. The tag indicates that it will grow inches every year. She also buys a tulip plant when it is inches tall. The tag indicates that it will grow inches a year. After how many years are the two plants the same height?

Possible Answers:

$6 \text{ years}$

$23 \text{ years}$

$16 \text{ years}$

$7 \text{ years}$

They will never be the same height at the same time.

Correct answer:

$6 \text{ years}$

Explanation:

We can express each plant's growth as a function of years in the following equations:

Rose height after x years = 3x+5

Tulip height after x years = 2x+11

Since we are looking for the year when the two plants are of equal height, we set these expressions for height equal to each other, and solve for x:

3x+5=2x+11

Combining like terms by subtracting 2x from both sides and subtracting 5 from both sides gives us:

x=6

The plants will reach the same height after 6 years of growth.

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Example Question #6 : Solving Expressions

Evaluate the expression if w = 3 , x = 8 , y = -2 and z = 2

$\frac{(y+z)^2}{xw}$

Possible Answers:

$\frac{2}{3}$

$\frac{16}{24}$

Correct answer:

Explanation:

After you plug in all of your given values the expression is as followed;

$\frac{(-2+2)^2}{8\cdot3}=\frac{0}{24}=0$

Since the numerator is zero, therefore, the entire fraction equals zero.

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Example Question #7 : Solving Expressions

Evaluate the expression if w = 3 , x = 8 , y = -2 and z = 2

$\frac{12w-6y}{z^2}$

Possible Answers:

Correct answer:

Explanation:

When you plug in your given values the expression should read as followed;

$\frac{12(3)-6(-2)}{2^2} = \frac{36+12}{4}=\frac{48}{4}=12$

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Example Question #1 : Solving Expressions

Simplify the expression

2(6c-8d)+3(4c-9d)

Possible Answers:

24c - 43d

- 43d

24c+43d

Correct answer:

24c - 43d

Explanation:

2(6c-8d)+3(4c-9d) = 12c -16d+12c-27d = 24c-43d

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Example Question #9 : Solving Expressions

Evaluate the expression $a^{2}-7a+4b$ when a=2 and b=7 .

Possible Answers:

Correct answer:

Explanation:

First, substitute for and for : $(2)^{2}-7(2)+4(7)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

4-7(2)+4(7)

4-14+28

Leaving you with,

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Example Question #10 : Solving Expressions

Evaluate the expression $-5+15-x-3x^{2}$ given x=5 .

Possible Answers:

Correct answer:

Explanation:

First, you substitute for : $-5+15-(5)-3(5)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

-5+15-5-3(25)

-5+15-5-75

Leaving you with,

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Algebra II : Solving Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Solving Expressions

Example Question #2 : Solving Expressions

Example Question #3 : Solving Expressions

Example Question #4 : Solving Expressions

Example Question #5 : Solving Expressions

Example Question #6 : Solving Expressions

Example Question #7 : Solving Expressions

Example Question #1 : Solving Expressions

Example Question #9 : Solving Expressions

Example Question #10 : Solving Expressions

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