SOLVING FOR VARIABLES!Learn the Simple Algebra of solving for numerous variables!

Lesson A1.2.2 “Finding a Formula”

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WHY DO WE SOLVE FOR VARIABLES? Solving for variables

helps us find what we are looking for.

When we are saying that we are looking for a number, we replace it with a variable.

Using a variable is an easier way to find the number we are looking for.

Variable Types-

Any Letter-oAoBoC…

Most commonly used letters are x and y.

Solving for X!Example-

X+4=8Goal: Get X by itselfSubtract 4 from each side:

X+4=8-4=-4

Rule: Whatever you do to one side you do to the other.

X=8-4When 4 was subtracted from the left X was left alone.

X=4

SIMPLICITY

As you can see, solving for X is quite simple. But problems will of course get harder. The previous example is one of the simplest

problems that you can have. Just remember the goal is to get X by itself

every time. Let’s try to do some different problems…

SOLVE FOR Y

2Y-8=2 *Remember the goal is to get Y by itself!

+8=+8 (First move the 8 by adding 8 to each side.)

2Y=2+8 (Add together 2 and 8.)2Y=10 (2+8 is 10. Now you still want to get Y

by itself.)2Y/2=10/2 (Divide by two, because 2 and Y

are being multiplied together and division is the opposite of multiplication.)

Y=5 (Dividing by 2 cancels the 2s, leaving Y alone, and dividing 10 by 2 leaves you with

5!)

JUST A COUPLE RULES

When moving a number from one side to another you must do the opposite of each sign.

Addition, opposite is subtraction. (Same with subtraction).

Multiplication, opposite is division.(Same with division).

Raising a number to a power, opposite is taking the root of the number. (Same with taking a root, raise to a number).

MULTIPLE VARIABLES

Now that you know how to do simple x and y problems, you can solve for more then one variable, when many are listed.

Simply do the same thing when solving, except combine numbers that have the same variable.

If you are not solving for the variable, and there is a number with the other variables, just move them accordingly with the variable.

EXAMPLE OF VARIABLE PROBLEM

Solve for G-(½)G+2t+6=-4+6t(½)G+2t-6=-4(-6)+6t ; First task to get G by

itself…so subtract 6 on both sides.

You should then get: (½)G+2t=-10+6t

Next-Still get G alone, by subtracting 2t from each side.(½)G-2t=-10+6t-2tYou should get: (½)G=-10+4t

Finally the last step to get G alone is the multiply by 2, since G is being divided by 2, and multiplication is the opposite of division.2(½)G=(-10+4t)2You end up with:

G=-20+8t!

EQ

UATIO

N F

OR

A

REA

!!!

You can also solve for a specified variable when given information.

Ex. From the given equation, express in

each term how you would solve for each.

A=LW (Area= Length times Width) Solve for both Length and Width

you divide Area for the specified variable.

Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L)

This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse.

SOLVING WITH A PICTURE

From the given information plug in the values for the area of the rectangle.

12

4

Area= Length x Width

Since Area Length times Width, just plug in your given values to find area.

A=LxWL=12 and W=4 (Define what each

variable equals first.) A=12x4

Solve!

Area is 48

IT’S TIME FOR A QUIZ!If at you do not know the answer, click on the button, and it will take you back to the practice question for a reference!To return to the quiz question click the button!

1. SOLVE FOR X

X+8=4

a. ½b. 4c. -4d. 12

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!

For the next question click-

Solving for X!Example-

X+4=8Goal: Get X by itselfSubtract 4 from each side:

X+4=8-4=-4

Rule: Whatever you do to one side you do to the other.

X=8-4When 4 was subtracted from the left X was left alone.

X=4

-To go back to quiz question click

2. SOLVE FOR X

2x-7=8

a. 7 ½b. 30c. ½d. 15

THAT’S RIGHT! CONGRATULATIONS!

For the next question click-

THAT’S WRONG!To go back and reference click-

To go back to question click-

Solving for X!Example-

X+4=8Goal: Get X by itselfSubtract 4 from each side:

X+4=8-4=-4

Rule: Whatever you do to one side you do to the other.

X=8-4When 4 was subtracted from the left X was left alone.

X=4

-To go back to quiz question click

3.SOLVE FOR G

6G+6t=24

a. G=84-36tb. G=4+t

c. G=4-36td. G=4-t

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go to the next question click-

EXAMPLE OF VARIABLE PROBLEM

Solve for G-(½)G+2t+6=-4+6t(½)G+2t-6=-4(-6)+6t ; First task to get G by

itself…so subtract 6 on both sides.

You should then get: (½)G+2t=-10+6t

Next-Still get G alone, by subtracting 2t from each side.½)G-2t=-10+6t-2tYou should get: ½)G=-10+4t

Finally the last step to get G alone is the multiply by 2, since G is being divided by 2, and multiplication is the opposite of division.2(½)G=(-10+4t)2You end up with:

G=-20+8t!

-To go back to quiz question click

4. CHOOSE WHICH EQUATION IS THE VOLUME OF A SQUARE.

a. V=LxWb. V=LxWxHc. V=(bh)/2

d. V=2Lx2Wx2H

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go to the next question click-

EQ

UATIO

N F

OR

A

REA

!!!

You can also solve for a specified variable when given information.

Ex. From the given equation, express in

each term how you would solve for each.

A=LW (Area= Length times Width) Solve for both Length and Width

you divide Area for the specified variable.

Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L)

This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse.

-To go back to quiz question click

5.SOLVE FOR THE HEIGHT OF THE RECTANGLE(ROUND TO THE NEAREST WHOLE NUMBER IF NECESSARY.)

a. 3b. 4c. 5d. 6

Total Volume= 360

h

12

6

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go back to the beginning click-

SOLVING WITH A PICTURE

From the given information plug in the values for the area of the rectangle.

12

4

Area= Length x Width

Since Area Length times Width, just plug in your given values to find area.

A=LxWL=12 and W=4 (Define what each

variable equals first.) A=12x4

Solve!

Area is 48

-To go back to quiz question click

6. SOLVE FOR Q

(½)Q+12t=6t-8+3r

a. Q=-3t-4+3/2rb. Q=-12t-16+6rc. Q=-18t-8+3rd. Q=-3t-4+1r

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go back to the beginning click-

SIMPLICITY

As you can see, solving for X is quite simple. But problems will of course get harder. The previous example is one of the simplest

problems that you can have. Just remember the goal is to get X by itself

every time. Let’s try to do some different problems…

-To go back to quiz question click

7. VOLUME OF THE CYLINDER

With the given equation for the volume of a cylinder solve for the radius.

a) r= v/∏hb) r=v/∏h

c) r=(v/∏h)2

d) r= v∏h

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go back to the beginning click-

EQ

UATIO

N F

OR

A

REA

!!!

You can also solve for a specified variable when given information.

Ex. From the given equation, express in

each term how you would solve for each.

A=LW (Area= Length times Width) Solve for both Length and Width

you divide Area for the specified variable.

Ex. In solving for Length it is L=(A/W) In solving for Width it is W=(A/L)

This is handy, because sometimes you may have two variables present and have to find the other, so you need to know how the equations work in reverse.

-To go back to quiz question click

8. TRUE OR FALSE?

Please answer either true or false to the following question.

A variable can be any letter?

TRUE or FALSE

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go to the next question click-

WHY DO WE SOLVE FOR VARIABLES? Solving for variables

helps us find what we are looking for.

When we are saying that we are looking for a number, we replace it with a variable.

Using a variable is an easier way to find the number we are looking for.

Variable Types-

Any Letter-oAoBoC…

Most commonly used letters are x and y.

-To go back to quiz question click.

9. SOLVING AREA

Solve the area of a triangle with the following formula:

A= (½)bh

a) A=96b) A=48

c) A=192d) A=24

8

12

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!To go back to the beginning click-

SOLVING WITH A PICTURE

From the given information plug in the values for the area of the rectangle.

12

4

Area= Length x Width

Since Area Length times Width, just plug in your given values to find area.

A=LxWL=12 and W=4 (Define what each

variable equals first.) A=12x4

Solve!

Area is 48

-To go back to quiz question click

10. TRUE OR FALSE

Please answer true or false to the following question.

Division is the opposite of raising a number to a power.

TRUE or FALSE

THAT’S WRONG!To go back and reference click-

To go back to question click-

THAT’S RIGHT! CONGRATULATIONS!(THE OPPOSITE OF DIVISION IS MULTIPLICATION!)

To go back to the beginning click-

JUST A COUPLE RULES

When moving a number from one side to another you must do the opposite of each sign.

Addition, opposite is subtraction. (Same with subtraction).

Multiplication, opposite is division.(Same with division).

Raising a number to a power, opposite is take the root of the number. (Same with taking a root, raise to a number).

-To go back to quiz question click