ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations

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1 ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1

2 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for key words such as 2-1 Writing Equations EXAMPLE 1: Translate each sentence into an equation a. Seven times a number squared is five times the difference of k and m. b. Fifteen times a number subtracted from 80 is 25. c. Two plus the quotient of a number and 8 is the same as 16. d. Twenty-seven times k is h squared decreased by 9. EXAMPLE 2: Translate the sentence into a formula a. The area of a triangle is equals the product of ½ the length of the base and the height. b. The perimeter of a square equals four times the length of a side. c. The density of an object is the quotient of its mass and its volume. EXAMPLE 3: Translate each equation into a sentence. a. b. c. 2

3 Solve for equations: 1. Using multiplication and division. 2. Using addition and subtraction. 2-2 Solving One- Step Equations Solve an Equation Equivalent Equations ADDITION SUBTRACTION MULTIPLICATION DIVISION 3

4 Solve for equations: 1. Involving more than one operations 2. Involving consecutive integers 2-3 Solving Multi- Step Equations To solve a multi-step equations, we must. To solve consecutive integer problems we must. What s number theory? 4

5 Solve for equations: 1. with variables on each side. 2. involving grouping symbols. 2-4 Solving Equations with variables on both sides. To solve an equation that has variables on both sides, use the addition or subtraction property of equality to write an equivalent equation with the variable on one side. If equations contain grouping symbols like parentheses or brackets, use the Distributive Property first to remove the grouping symbols. Or use the multiplication or division properties of equality to remove the grouping symbols. Steps for Solving Any Equations: 1. Use the Distributive Property first if there are parentheses. If there is a fraction bar, it may be helpful to multiply the entire equation by a common denominator. 2. Simplify each side of the equation by adding like terms. 3. If there is a variable on both sides of the equations, then get the variable on one side of the equation. 4. Move the constants to the other side of the equation. 5. Divide. You are trying to isolate the variable. 5

6 2-4 Example 1: 11x 4 = 29 Try it Example 3: Solving Equations with variables on both sides. Example 2: Example 4: Example 5: Example 6: Seventeen equals thirteen subtracted from six times a number x. 6

7 1. Evaluate expressions with absolute vale. 2. Solve equations involving absolute value. 2-5 Solving Absolute Value Equations Simple Absolute Value Concepts: Solution Set Notation: 7

1. Compare ratios. 2. Solve proportions. Ratio Define it Proportion 2-6 Ratios and Proportions Ways to express ratios What do proportions look like? Determine whether the ratios are equivalent.

8 1. Compare ratios. 2. Solve proportions. Ratio Define it Proportion 2-6 Ratios and Proportions Ways to express ratios What do proportions look like? Determine whether the ratios are equivalent. Special names for terms in proportions : (The numerators and the denominators are by the same number) and and EX. 1 EX. 3 EX and and 3 24 Learn it 1.5 and 1.2 are called the. They are the middle terms of the proportion..02 : 1.5 = 1.2 : and 9.0 and 1.2 are called the. They are the first and last terms of the proportion. Solve Proportions using Cross Products: CROSS PRODUCTS ARE NOT Means and Extremes To solve a proportion using cross products, write an equation that s sets the product of the extremes equal to the product of the means. EX. 1 r

Seven is less than 11. Four more than seventeen. Four is not equal to three.

Seven is less than 11. Four more than seventeen. Four is not equal to three. Prealgebra.1: Translations, Simplifying and Evaluating Expressions Words such as,, and indicate addition. Words such as,, and indicate subtraction. Translate each of the following into mathematical symbols.