Solving Literal Equations

1.5: Literal Equations

Goals:

Solve equations for a specific variable

Evaluate equations for a specific variable

Review 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?

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

AREA BASE HEIGHT

Rules to Solving Literal Equations Solving equations for a specific variable involve the same rules as solving an equation.

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: Solve the following for y In other words, isolate the variable “ y ” by itself Undo the subtracting 5x by adding 5x to both sides. Undo the multiplying by 2, by dividing both sides by 2 Remember, all numbers on the other side get divided by 2. Since you have “ y = “, you have now solved for y

Example: Solve the same equation for x In other words, isolate the variable “ x ” by itself Undo the positive 2y by subtracting 2y from both sides. Undo the multiplying by -5, by dividing both sides by -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.

Formula 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 “ r ”

Formula Examples:

Since “r” is being multiplied by both the “2” and “  ” you would divide by “ 2  ”

Formula Examples:

Since the equation now reads:

“ r = “

the equation is solved.

Solve the following formula, the perimeter of a rectangle for “ w ” In other words, isolate the variable “ w ” by itself Undo the positive “2 l ” by subtracting “2 l ” Undo the multiplication by dividing both sides by 2 Remember, all the numbers get divided by 2

Examples: On Your Own 1) ; Solve for b 2) ; Solve for y 3) ; Solve for y

Examples: On Your Own