MAT.105X A3

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MAT.105X A3

Solve an Equation for a Specific Variable

Treat all variables you are not solving for as constants.

Solve a Linear Inequality in One Variable

Compound Inequality

Three parts: all operations must be performed on each of the three parts

Solutions

Write in inequality notation

Graph on a number line

Write in set notation

Write in interval notation

The process is mostly the same as for solving linear equations in one variable. However,

when we multiply or divide both sides of the inequality by a negative number we must reverse the direction of the inequality symbol.

Linear Inequality in One Variable

A linear inequality in one variable can be written in the form

ax+b<c,

ax+b<=c,

ax+b>c, or

ax+b>=c,

where a, b, and c are real numbers and a is not zero.

Solve Compound Inequalities Containing And or Or

Or / Union

Take everything (but only take things that overlap once)

And / Intersection

Take the overlap

Solve Applied Problems

Simple Interest

I=PRT

I=interest earned (simple)

P=principal (initial amount invested)

R=annual interest rate (expressed as a decimal)

T=amount of time the money is invested (in years)

Read the problem carefully. Then read it again. Draw a picture, if applicable.

Identify what you are being asked to find. Define the variable; that is, assign a variable to the unknown quantity. Also,

Translate from English to math. Some suggestions for doing so are

Solve the equation.

Interpret the meaning of the solution as it relates to the problem. If there are other unknowns, find them. State the answer in a complete sentence. Be sure your answer makes sense in the context of the problem.

Solve a Linear Equation with No Solution or an Infinite Number of Solutions

Infinite Number of Solutions

An equation has an infinite number of solutions if an identity results from the solution process.

We say the solution set is the set all real numbers.

No Solution

An equation has no solution if a contradiction results from the solution process.

We say the solution set is the empty set.

Solve a Linear Equation

Linear Equation

A linear equation in one variable is an equation that can be written in the form ax+b=0 where a and b are real number and a is not zero.

Process

Equation

An equation is a mathematical statement that two expressions are equal.

We can solve equations.

We can simplify expressions. Expressions do not contain an equal sign (=).

Properties

Let a, b, and c be real numbers.

Solve an Equation

To solve an equation means to find the value or values of the variable that make the equation true.