HOW TO SOLVE FOR A VARIABLE

IN A GIVEN EQUATION

Lesson Plan

TABLE OF CONTENTS1. First Step2. Applying the First Step3. Second Step4. Now You Try!5. Part 2: Solving for x in a Quadratic Equation6. Finding the Zeroes/Roots7. Solve for x once again8. Practice Problem9. Quiz – Question #110. Question #211. Question #312. Question #413. Question #514. Question #615. Question #716. Question #8

FIRST STEP Lets use the example x + 12 = 4x. In

this problem we are solving for the variable x.

The first thing we want to do is get all the like terms together by putting all the plain numbers on one side of the equal sign, and put all the numbers with an x attached to them on the other side of the equal sign.

APPLYING THE FIRST STEP We will get all the like terms together through

adding and subtracting.

In our example of x + 12 = 5x we will subtract the x from the left side of the equal sign to cross out the x.

Then we subtract the x from the right side of the equal sign as well.

Whatever we do to the left side of the equal

sign, we do the same operation to the right side.

SECOND STEP We now have 12 = 4x after subtracting x from both

sides.

The next step is to get x alone in this equation.

We do this by dividing the right and left sides of the equation by whatever number is multiplied by x.

In our example we would divide both sides by 4 to get x = 3 because 4 divided by 4 equals x and 12 divided by 4 equals 3.

x = 3 is our answer!

NOW YOU TRY!If 6x - 12 = 4x + 6 then solve for x.

Click on the correct answer!

a) x = 3 c) x =9

b) x = -3 d) x = -6/10

CORRECT! Go to Part 2 of the LessonQuiz: Go to Question #2 Go to Question #3 Go to Question #4 Go to Question #5 Go to Question #6 Go to Question #7 Go to Question #8

TRY AGAIN! If you need help, go back to the Table of Contents to find

what you need to review.

Back to You Try! Back to Practice ProblemQuiz: Back to Question #1 Back to Question #2 Back to Question #3 Back to Question #4 Back to Question #5 Back to Question #6 Back to Question #7 Back to Question #8

PART 2: SOLVING FOR X IN A QUADRATIC EQUATION This is called finding the “zeroes” or “roots”

of the equation. In exact terms, we are finding where the graph any given equation crosses the x-axis.

Here we will work with the example: x² + 5x + 6 = 0

FINDING THE ZEROES/ROOTS First, we need to find 2 numbers that add to

the middle term in the equation and also multiply to the third term in the equation.

In our example of x² + 5x - 6 = 0 these two numbers are 6 and -1 because 6 + -1 = 5 (the middle term) and 6 x -1 = -6 (the third term).

Now we insert the two numbers we found into

(x± ) (x± ) = 0

SOLVE FOR X ONCE AGAIN We just “unfoiled” the equation x² + 5x - 6 =

0 to be (x + 6) (x – 1) = 0

Now we simply solve for x treating the contents of both parenthesis as separate equations equaling zero.

Therefore, x + 6 = 0 and x – 1 = 0.

When we solve for x we get zeroes of x = -6 and x = 1. That’s our answer! Now lets practice!

PRACTICE PROBLEMIf x² + 5x + 6 = 0 then what are the

zeroes of this equation?

a) x = 2, x = 3 c) x = -2, x = -3

b) x = 6, x = -1 d) x = -6, x = 1

QUIZ! – QUESTION #1If 20x + 35 = 2 + 31x then solve for x.

a) x = 3 c) x = 37/51

b) x = 51/37 d) x = 1/3

QUESTION #2If 50x + 200 = 300 + 25x then solve for

x.

a) x = 20 c) x = 4

b) x = 1/4 d) x = 5

QUESTION #3If x² + 3x - 28 = 0 then what are the

zeroes of this equation?

a) x = 4, x = 7 c) x = -4, x = 7

b) x = 4, x = -7 d) x = -4, x = -7

QUESTION #4If x² - 8x + 12 = 0 then what are the

zeroes of this equation?

a) x = 6, x = 2 c) x = -6, x = 2

b) x = 6, x = -2 d) x = -6, x = -2

QUESTION #5If 30x + 75 = 125 + 5x then solve for x.

a) x = 8 c) x = 200/35

b) x = 2 d) x = 50/35

QUESTION #6If x² + 8x + 40 = 0 then what are the

zeroes of this equation?

a) x = -8, x = -5 c) x = 8, x = -1

b) x = 8, x = 5 d) x = -8, x = 1

QUESTION #7If 8x + 7 – 4x = 27 – 12x + 5 then solve

for x.

a) x = 25/39 c) x = -8/39

b) x = 2 d) x = 25/16

QUESTION #8If x² + 8x - 48 = 0 then what are the

zeroes of this equation?

a) x = 12, x = 4 c) x = 12, x = -4

b) x = -12, x = -4 d) x = -12, x = 4

CONGRATULATIONS!!!

YOU FINISHED THE LESSON!!!