Algebraic Equations

Unit Review Sheet

Facts and Definitions

Lesson 1: Algebraic Equations

• An algebraic expression is a mathematical phrase made up of variables, constants, and mathematical operations (like addition, subtraction, multiplication, and division).
• A mathematical equation is a number sentence that includes an equal sign (=) joining two expressions. The equal sign shows that the value of the expressions is the same.
• A solution in algebra is the value that can be assigned to the variable to make the equation true.
• "Guess and check" is an acceptable method that can be used to find the value of a variable in an equation.
• The symmetric property of equality says that if a = b, then b = a. This property allows you to flip the position of two expressions around the equal sign. For example, 2 + n = 8 could be written as 8 = 2 + n.
• Word problems may sometimes contain numerical information that is not needed for writing an equation and solving the problem.

Lesson 2: Solving One-Step Equations, Part 1

• Tape diagrams and hanger diagrams are useful tools for understanding and solving algebraic equations.
• Adding the same number to both sides of an equation keeps the equation balanced.
• Subtracting the same number from both sides of an equation keeps the equation balanced.
• Inverse operations are mathematical operations that undo each other. Addition and subtraction are inverse operations, as are multiplication and division.
• Additive inverses can be used to solve equations containing addition and subtraction.

Lesson 3: Solving One-Step Equations, Part 2

• Inverse operations are mathematical operations that undo each other. Multiplication and division are inverse operations, just like addition and subtraction are.
• Multiplying both sides of an equation by the same value allows the two sides to remain equal.
• Dividing both sides of an equation by the same value allows the two sides to remain equal.

Lesson 4: Solving Two-Step Equations

• To solve two-step equations, you use the order of operations in reverse.
• Inverse operations are used to "cancel out" a number. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
• Equations that contain decimal numbers and fractions are solved using the same steps as equations that contain integers.

Lesson 5: Inequalities

• An inequality is a mathematical statement that shows the relationship between two values that may or may not be equal.
• A mathematical inequality has an infinite number of solutions that make the inequality true.
• The set of all values that makes an inequality true is called the solution set.
• The solution set for an inequality can be graphed on a number line.

Lesson 6: Solving Inequalities

• A mathematical inequality has an infinite number of solutions that make the inequality true.
• When working with an inequality, you can switch the placement of the expressions as long as you also switch the direction of the inequality sign.
• Inverse operations are used to solve inequalities in the same order they are used to solve equations.
• While the mathematical solution set for an inequality word problem may be infinite, the reasonable answers for a word problem may be limited.

Lesson 7: Independent and Dependent Variables

• In a two-variable equation, the independent variable is the variable that can cause a change in the value of the other variable. This variable is usually connected to a numeral by addition, subtraction, multiplication, or division.
• In a two-variable equation, the dependent variable is the variable that depends on the value of the other variable. This variable is usually by itself on one side of the equal sign.
• Two-variable equations have an infinite set of solutions.
• Input/output tables and "guess and check" are useful tools for finding solutions to two-variable equations.
• Two-variable equations (without exponents) are called linear equations, and coordinate grids are used to graph their solution sets. The graphed solution set for a linear equation is always a straight line.

Lesson 8: Unit 5 Test

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Final Project: All About Me

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