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Simplifying 5(10 + -1(19 + -0.5z) + -1z) + (5(19 + -0.5z)) + 5z = 100 5(10 + (19 * -1 + -0.5z * -1) + -1z) + (5(19 + -0.5z)) + 5z = 100 5(10 + (-19 + 0.5z) + -1z) + (5(19 + -0.5z)) + 5z = 100 Combine like terms: 10 + -19 = -9 5(-9 + 0.5z + -1z) + (5(19 + -0.5z)) + 5z = 100 Combine like terms: 0.5z + -1z = -0.5z 5(-9 + -0.5z) + (5(19 + -0.5z)) + 5z = 100 (-9 * 5 + -0.5z * 5) + (5(19 + -0.5z)) + 5z = 100 (-45 + -2.5z) + (5(19 + -0.5z)) + 5z = 100 -45 + -2.5z + ((19 * 5 + -0.5z * 5)) + 5z = 100 -45 + -2.5z + ((95 + -2.5z)) + 5z = 100 -45 + -2.5z + (95 + -2.5z) + 5z = 100 Remove parenthesis around (95 + -2.5z) -45 + -2.5z + 95 + -2.5z + 5z = 100 Reorder the terms: -45 + 95 + -2.5z + -2.5z + 5z = 100 Combine like terms: -45 + 95 = 50 50 + -2.5z + -2.5z + 5z = 100 Combine like terms: -2.5z + -2.5z = -5z 50 + -5z + 5z = 100 Combine like terms: -5z + 5z = 0 50 + 0 = 100 50 = 100 Solving 50 = 100 Couldn't find a variable to solve for. This equation is invalid, the left and right sides are not equal, therefore there is no solution.
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