a.4a solving literal equations and formulas

A.4a Solving Literal Equations and

Formulas

Objectives:

• A.4a Solve literal equations (formulas) for a

specified variable

A.4a Solving Literal Equations 9/14/2016

Preliminaries

9/14/2016 A.4a Solving Literal Equations

x4

1

abc3

2

2

42 yx

2

32 yx

Definitions:

• An equation is a mathematical sentence that contains an equal sign ( = ).

Ex: 2x + 5 = 23

• A literal equation is an equation that contains 2 or more variables.

Ex: A = lw P = 2l + 2w

A.4a Solving Literal Equations

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What it means to solve:

• To solve for x would mean to get x by itself

on one side of the equation, with no x’s on

the other side. (x = __ )

• Similarly, to solve for y would mean to get

y by itself on one side of the equation, with

no y’s on the other side. (y = __ )

A.4a Solving Literal Equations 9/14/2016

Steps to follow

Step 1: Identify the variable to be isolated

Step 2 : Use inverses.

If possible use addition or subtraction first,

then multiplication or division

A.4a Solving Literal Equations 9/14/2016

Solve C = 2a + 2b for a.

A.4a Solving Literal Equations

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Solve X = 2y + 7z for z. Your Turn

A.4a Solving Literal Equations

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Solve ax + by = 10 for y.

Solve 8x – 5y = 12 for x. My Turn

A.4a Solving Literal Equations

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Solve 3y – x = 7 for x. Your Turn

A.4a Solving Literal Equations

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Ex: Solve 2x - 4y = 7 for x.

Your Turn

A.4a Solving Literal Equations

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Solve 8y – 4x = 12 for x. My Turn

A.4a Solving Literal Equations

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Your Turn

Solve 3x + 2y = 5 for y.

A.4a Solving Literal Equations

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Another example:

Solve for h.

hrV 2

Another example:

• Solve for b.

5

2 bxy

A.4a Solving Literal Equations

Solve for C.

325

9 CF

Another example:

Solve for b.

bhV3

1

A.4a Solving Literal Equations

Another example:

Solve for x.

zxyV 2

4

1

A.4a Solving Literal Equations

Inverse of

• Power of 2

• Power of 3

9/14/2016 A.4a Solving Literal Equations

3

Another example:

Solve for y.

zxyV 2

4

1

Your Turn

1. Solve 3x - 9y = 15 for x

2. Solve 3x - 9y = 15 for y

3. Solve for y, y a

3 c

A.4a Solving Literal Equations

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Solve 3x - 9y = 15 for x

Solve 3x - 9y = 15 for y

Solve for y,

y a

3 c

Solve for x.

153

2 xy

A.4a Solving Literal Equations

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Solve a(y + 1) = b for y (another way)

Solve d = 2w ( 10 + x )for x (another way)

A.4a Solving Literal Equations

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Solve Solve