 # Warm up Simplify: -(2x + 3) + 4(x + 2) A – 2 – ( 3 + a) Solve: 13m – 22 = 9m -6.

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Warm up Simplify: -(2x + 3) + 4(x + 2) A – 2 – ( 3 + a) Solve: 13m – 22 = 9m -6

Ch. 3.3 (continued) An equation with all real numbers as a solution Solve: 6x + 2 = 2(3x + 1) 6x + 2 = 6x + 1 Notice that for all values of x, the statement 6x + 2 = 6x + 2 is true. The equation has every number as a solution. Example 2 7(2p + 1) = 14p + 7 14p + 7 = 14p + 7All real numbers ANSWER: All real numbers

Ch. 3.3 (continued) An equation with no solution Solve: 5(2x + 1) = 10x 10x + 5 = 10x -10x -10x 5 = 0 The statement 5 = 0 is not true, so the equation has no solution. Example 2: 25t = 5(5t + 1) 25t = 25t + 5 -25t -25tNO SOLUTION 0 = 5

Practice! Solve the equation but remember, it may have a solution, no solution, or all real numbers! 3x + 6 = 3(2 + x)

Practice! Solve the equation but remember, it may have a solution, no solution, or all real numbers! -24s – 53 = 39 – s

Practice! Solve the equation but remember, it may have a solution, no solution, or all real numbers! 16s = 4(4s – 3)

Practice! Solve the equation but remember, it may have a solution, no solution, or all real numbers! 36x + 6 = 6(6x + 1)

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