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Advanced Algebra - Trigonometry Objective: SWBAT solve linear equations. 1 Warm Up Simplify: 1. 8b - 3( 4 – b ) 2. -6 (m – 9) + 14m – 20 3. 2 (b + 5) + 3 (2b – 10) 4. -w3 + w2 - 7 w2 - 8w3 5. 7t (t2 + 2) + 9t (t – 2) 2 Vocabulary Equation: a statement that two expressions are equal. Ex. x + 2 = 9, x2 – 4x +10 = 0, Solution: all numbers that make an equation true. Solution Set: the set of all the solutions of an or condition. Equivalent Equations: equations with the same solution set Ex. x + 1 = 5 and 6x + 3 = 27 Linear Equation: a linear equation in one variable has the form ax + b = c (aka first degree equation) 3 Which of the following are a linear equations? a. 3x - 7=12 b. 24x + 5 = 5(x – 2) c. 2x - 7x2 + 4x3 = 19 d. 12x + 3= -4x-8 e. 4 5 x + 8 = 20 f. 1 = −8 4 Solve an equation with variable on one side. 2 x7 5 3 5 Solve an equation with variable on both sides. Solve: 8y – 16 = 13y + 9 6 Solve an equation using the distributive property. Solve: 4(2x – 9) + 5x = -3(10 – x) 7 Solve an equation with clearing a fraction. Solve: 2t 4 1 1 7 t t 3 2 4 3 8 Additional Vocabulary Identity: an equation that is satisfied by every number Conditional Equation: an equation that is satisfied by some numbers but not others Contradiction: an equation that has no solution and the solution set is an empty set or null set. {0}. 9 Identify the Type of Equation. Decide whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. a. -2(x + 4) + 3x = x – 8 b. 5x – 4 = 11 c. 3(3x-1) = 9x +7 10 Homework. Page 440 – Appendix A # 2-22 evens 11