solving literal equations

1.5: Literal Equations1.5: Literal EquationsGoals: 1)Solve equations for a specific variable2)Evaluate equations for a specific variable

ReviewReviewWhat it means to solve equations:What it means to solve equations:

To solve an equation for x means to get x by itself on one side of the equation.

( x = _____ )

To solve an equation for y means to get y by itself on one side of the equation.

( y = _____ )

Therefore, to solve for any variable is to get it by itself on one side of the equation.

What are Literal Equations?What are Literal Equations?

A literal equation is an equation with more than one variable.

bhA21

AREA BASE HEIGHT

1852 xy

Rules to Solving Literal EquationsRules to Solving Literal Equations

Solving equations for a specific variable involve the same rules as solving an equation.

1. Simplify each side of the equation, if needed, by distributing or combining like terms.

2. Move the variable being solved for to one side of the equation by using the opposite operation of addition or subtraction.

3. Isolate the variable being solved for by itself by applying the opposite operation to each side.a. First, use the opposite operation of addition or subtraction to

move any other constants or variables to the other side. b. Second, use the opposite operation of multiplication or

division to eliminate the coefficient of the variable being solved for.

Example: Example: Solve the following for Solve the following for yy

1852 xy In other words, isolate the variable “ y ” by itself

x5 x5xy 5182

Undo the subtracting 5x by adding 5x to both sides.

xy259

Undo the multiplying by 2, by dividing both sides by 2

2 2Remember, all numbers on the other side get divided by 2.

Since you have “ y = “, you have now solved for y

Example: Example: Solve the same equation for xSolve the same equation for x

1852 xy In other words, isolate the variable “ x ” by itself

y2 y2yx 2185

Undo the positive 2y by subtracting 2y from both sides.

5218

yx

Undo the multiplying by -5, by dividing both sides by -5

5 5 Remember, all numbers on the other side get divided by -5.

Since you have “ x = “, you have now solved for x

Move the negative to the numerator by changing all the signs.

5218 yx

Formula Formula Examples:Examples:Solving literal equations allows you to transform formulas (such as area, volume, perimeter, etc) so you can solve for any of the parts:

Solve the following formula for “Solve the following formula for “rr””

rC 2

Formula Formula Examples:Examples:Since “r” is being

multiplied by both

the “2” and “ ”

you would divide by

“ 2 ”


rC 22 2

rC 2

Formula Formula Examples:Examples:Since the equation now reads:

“ r = “

the equation is solved.


rC 22 2

rC 2

Solve the following formula, the perimeter of Solve the following formula, the perimeter of a rectangle for “ w ”a rectangle for “ w ”

wlP 22 In other words, isolate the variable “ w ” by itself

l2l2 Undo the positive “2l” by subtracting “2l”

wlP 22 Undo the multiplication by dividing both sides by 2

2 2wlP

2

Remember, all the numbers get divided by 2

Examples:Examples:On Your OwnOn Your Own

bhA21

1) ; Solve for b

2) 24)4(3 yx ; Solve for y

3) 1025 zxy ; Solve for y


1) Solve for b: A = ½bh

2) Solve for y: 3(x-4y) = 24

3) Solve for y: 5xy + 2z = 10

bhA21

bhA2

bhA

2



2) Solve for y: 3(x-4y) = 24


24)4(3 yx

24123 yx

xy 32412

12324

xy

42 xy



2) Solve for y: 3(x-4y) = 24


1025 zxy

zxy 2105

xzy

5210

xzy522

solving literal equations

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