Solving Algebra Equations

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Presentation transcript:

Solving Algebra Equations Objective: To solve all kinds of algebra equations.

Solving Equations When solving algebraic equations, we will do the same things in the same order each time. Our goal is to isolate the variable. We will do this by getting all terms with letters (variables) on one side and all terms that are just numbers (constants) on the other. We will follow this procedure.

Solving Equations We will get all terms with a variable on the one side and all terms without a variable on the other side. We will do this using addition and subtraction. We will then make the variable have a coefficient of one. We will do this using multiplication and division.

Example 1 Find the solution for the following equation.

Example 1 Find the solution for the following equation. Subt 3 from both sides Divide both sides by 2

Example 3 Find the solution for the following equation. When working with fractions, it is often easier to get rid of the fraction first. In this problem, we will do this by multiplying both sides by 3.

Example 3 Find the solution for the following equation. When working with fractions, it is often easier to get rid of the fraction first. In this problem, we will do this by multiplying both sides by 3.

Class work Page 91 11-21 odd 27-33 odd

Homework Pages 91-92 12-22 even 26-50 even

Multi-Step Equations When solving more complex equations, you should always simplify each side of the equation first before you start to move things. Then, use our rules from before.

Example 1 Solve the following equations.

Example 1 Solve the following equations. Combine like terms Add 23 to both sides Divide by 7 Solve

Got it? Solve the following equations.

Got it? Solve the following equations.

Got it? Solve the following equations.

Example 3 Solve the following equations.

Example 3 Solve the following equations.

Example 4 Solve the following equations. When solving equations with fractions, first find the common denominator. Then, multiply both sides by the common denominator to get rid of the fractions! What is the common denominator?

Example 4 Solve the following equations.

Got it? Solve the following equations.

Got it? Solve the following equations.

Got it? Solve the following equations.

Class Work Page 98 12, 14, 16 22, 24, 26 32, 34, 36 46, 48, 52

Homework Page 98 21-37 odd 45-53 odd

Variables on Both Sides When solving equations with variables on both sides, I like to get the variables on the left side and the constants on the right.

Variables on Both Sides When solving equations with variables on both sides, I like to get the variables on the left side and the constants on the right.

Example 3 Solve the following equation. Remember, we will simplify each side first.

Example 3 Solve the following equation. Remember, we will simplify each side first.

Got it? Solve the following equations.

Got it? Solve the following equations.

Got it? Solve the following equations.

Strange Answers Sometimes after doing your work, you will get an answer that is different from most others. If you get a statement that is always true, the answer to the original problem is all solutions. This is called an identity.

Strange Answers Sometimes after doing your work, you will get an answer that is different from most others. If you get a statement that is always true, the answer to the original problem is all solutions. This is called an identity. If you get a statement that is always false, the answer to the original problem is no solution.

Problem 4 Solve the following equation.

Problem 4 Solve the following equation. This statement is always true. This is an identity. The answer is all solutions.

Problem 4 Solve the following equation.

Problem 4 Solve the following equation. This statement is always false. The answer is no solutions.

Class Work Pages 105-106 10, 12, 14, 22, 24, 26, 28, 30, 32

Homework Pages 105-106 11-17 odd 21-37 odd

Literal Equations Solve for x.

Literal Equations Solve for x.

Literal Equations Solve for x.

Got it? Solve the following equation for m. What is the value of m when n = -2?

Got it? Solve the following equation for m. What is the value of m when n = -2? Add 5n to both sides Divide both sides by 2

Got it? Solve the following equation for m. What is the value of m when n = -2? Add 5n to both sides Divide both sides by 2 Replace n with -2.

Example 3 Look at page 110. There are several formulas that you will be using. You should be familiar with most of these.

Example 3 What is the radius of a circle with circumference 64 ft? Round to the nearest tenth.

Example 3 What is the radius of a circle with circumference 64 ft? Round to the nearest tenth.

Class Work Page 112 12, 14, 16, 20, 22, 24

Homework Page 112 11-17 odd