Algebra II : Solving Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Solving Expressions

Solve for x.

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

Example Question #2 : Solving Expressions

If , simplify .

Possible Answers:

Correct answer:

Explanation:

First, you substitute  for

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:

Example Question #3 : Solving Expressions

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

First, substitute 2 for z:.

Then, simplify: .

Next, you must isolate y by moving all other numbers and variables to the other side of the equation: , which gives you .

And simplify: .

Here, we then take the square root of both sides: .

Simplfy: , because both  and .

Example Question #4 : Solving Expressions

Simplify  given  and .

Possible Answers:

Correct answer:

Explanation:

First, substitute 1 for z, 2 for x and 3 for y:  and simplify: .

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we simplify the multiplication: .

Then add and subtract from left to right: .

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:

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

Correct answer:

Explanation:

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

Rose height after x years = 

Tulip height after x years = 

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:

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

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

Example Question #6 : Solving Expressions

Evaluate the expression if , ,  and 

Possible Answers:

Correct answer:

Explanation:

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

 

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

Example Question #7 : Solving Expressions

Evaluate the expression if , ,  and 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #8 : Solving Expressions

Simplify the expression

Possible Answers:

-

Correct answer:

Explanation:

Example Question #9 : Solving Expressions

Evaluate the expression  when  and .

Possible Answers:

Correct answer:

Explanation:

First, substitute  for  and  for 

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

Leaving you with,

Example Question #10 : Solving Expressions

Evaluate the expression  given .

Possible Answers:

Correct answer:

Explanation:

First, you substitute  for 

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

Leaving you with,

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