7 Solving Linear Equations

Linear equations are the simplest equations; yet they are the most useful equations in all of mathematics because you can always solve a linear equation. In linear equations the variable is to the first power. They are called linear because when we graph them, they produce a straight line. We use them everywhere to calculate a tip, interest on a loan, or speed for a car. If you really understand how to solve linear equations, then you will understand algebra.

7.1 Algebraic Expressions

- Evaluate algebraic expressions using substitution.
- Simplify algebraic expressions by combining like terms.
- Simplify algebraic expressions by multiplying monomials.
- Simplify algebraic expressions using the distributive property.

• Evaluating Algebraic Expressions

• Combining Like Terms

• Multiplying Monomials

• The Distributive Property

7.2 Solving Linear Equations

- Solve linear equations using additive and multiplicative inverse operations.
- Simplify equations with variables on both sides before solving.

• Solve x+b=c

• Solve ax=c

• Solve ax+b=c

• Convert to ax+b=c Form

7.3 Solving Linear Equations with Rationals

- Solve a variety of linear equations with fractional coefficients.
- Solve a variety of linear equations with decimal coefficients.

• Equations with Decimals

7.4 Linear Inequalities, Absolute Value Equations & Sets

- Graph inequalities of the form x>a, x>a, x<a, x<a, on a number line.
- Solve linear inequalities and graph the solution on a number line.
- Solve equations involving absolute value, for example k|ax+b|=c.
- Identify sets of real numbers described in verbal, roster, set builder, and graphical form.
- Identify the union and intersection of sets of real numbers described in various forms.

• Graphing Inequalities

• Solving Linear Inequalities

• Absolute Value Equations

• Sets

• Union & Intersection

7.5 Additional Assignments

- Translate English sentences into mathematical equations to solve problems.
- Determine upper and lower limits of a tolerance interval using absolute value.
- Identify the missing quantity needed to solve a mixture problem.
- Apply the simple annual interest formula I=pr to solve investment problems.
- Apply the distance formula d=rt to solve motion problems.
- Determine a salespersons commission as a percentage of total sales.