Section 1.4 Solving Equations

The Language of algebra provides a way to translate word expressions into mathematical equations 1)Write each equation as I read them a) b) c)

Def: Variables are used to represent numbers that are not known. Def: An open sentence that states that two mathematical expressions are equal is called an equation. Def: To solve an equation, you find the values of the variable that make the equation true. Those values are called solutions.

In order to solve an equation we may only use appropriate properties.

PropertyFor any real numbers Reflexive Symmetric Transitive Substitution a = a If a = b then, If a = b and b = c then, a = c b = a If a = b then, you can substitute b for a Sym Ref Trans Subs

Addition Property of Equality: if a = b then: a + c = b + c Subtraction Property of Equality: if a = b then: a - c = b - c Multiplication Property of Equality: if a = b then: a * c = b * c Division Property of Equality: if a = b then: a / c = b / c Properties of Equality: c ≠ 0 Any restrictions here? You can’t divide by 0

2.) Solve and name the property a.) x + 9 = b) 28 = 6y+4 c) r +(6+9) = 32

3.) Solve and name the property: 3(2a + 25) - 2(a - 1) = 78

Solve using the problem-solving plan 1. Read the problem 2. Plan the solution 3. Solve the problem 4. Check to see if answer is reasonable

Homework Page 31 Problems: #19 – 30 all, (odd), 57 and 63