Solving Expressions - Algebra 2

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

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.

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:

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 .

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: .

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.

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

First, you subsitute for and for :

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

Leaving you with,

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,

First, you substitute for :

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

Leaving you with,

First, substitute for , for , and for :

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

Leaving you with,

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,

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,

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,

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,

First, substitute for , for , and for :

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

Leaving you with,

First, substitute for , for , and for :

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

Leaving you with,

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,

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,