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1.) 3x – (4 – 2x) = 3(x + 4) x 2 # -4 3 5x -4 3x – 4 + 2x = 3x + 12 5x – 4 = 3x + 12 -3x -3x 2x – 4 = 12 +4 +4 2x = 16 2 2 x = 8 CA Standards: 4.0: Students simplify expressions before solving linear equations in one variable. 12.0: Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. Objective: Students simplify expressions and use inverse operations to solve equations. Agenda 1.) Warm-Up 2.) Lesson – No Solution/All Real Numbers 3.) Worksheet: Solving Linear Equations 1 What about this? 2(6x + 8) = 4(4 + 3x) 12x + 16 = 16 + 12x -12x -12x First, Distribute Collect like terms? No Move the smaller variable. • Do the Opposite! 16 = 16 ***Special case*** If the variables cancel out, and the number is the same on both sides, the answer is ALL REAL NUMBERS. This means no matter what number you substitute for x, the problem will always work out. And this? 4(6x + 7) = 8(4 + 3x) 24x + 28 = 32 + 24x -24x -24x 28 = 32 ? First, Distribute Collect like terms? No Move the smaller variable. • Do the Opposite! ***Special case*** If the variables cancel out, and the numbers on the two sides are different, then there is NO SOLUTION. This means no matter what number you substitute for x, the problem will never work out. Your Turn!!! 2(8x – 6) = 4(3 + 4x) 16x – 12 = 12 + 16x -16x -16x -12 = 12 Are they the same? No Solution First, Distribute Collect like terms? No Move the smaller variable. • Do the Opposite! NO WAY