Solving Linear Equations Lesson 1.3

Vocabulary Equation-a statement in which two expressions are equal. Linear Equation-an equation that can be written in the form ax=b where a and b are constants and a ≠ 0. Solution of an Equation in 1 Variable-a number that, when substituted for the variable, makes the equation a true statement. Equivalent Equations-equations that have the same solution.

Transformations that Produce Equivalent Equations Addition Property: add same number to both sides Subtraction Property: subtract the same number from both sides Multiplication Property: multiply both sides by the same nonzero number Division Property: divide both sides by the same nonzero number

Example 1: Solving an Equation with a Variable on One Side A) 5x – 16 = 24B)

Example 2: Solving an Equation with a Variable on Both Sides A) 5x – 7 = 3x – 3B) 15n – 8 = 5n + 2

Example 3: Using the Distributive Property A) -3(x+8)=2(x+3)+10xB) 5(x-2)=-4(2x+7)+x

Example 4: Solving an Equation with Fractions A)B)

Example 5: Writing and Using Linear Equations A) A waitress has a base salary of $2.65 per hour and makes about $15 per hour in tips. How many hours must she work to make $264.75? B) A car salesperson’s base salary is $21,000. She earns 5% commission on sales. How much must she sell to earn $65,000 total?

Example 5 continued C) The state sales tax in Michigan is 6%. If your total bill at dinner was $26.50, how much was dinner before tax was added on?