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Simplifying (15x + -7y + 18z) + -1(32x + 24y + -6z) = 0 Remove parenthesis around (15x + -7y + 18z) 15x + -7y + 18z + -1(32x + 24y + -6z) = 0 15x + -7y + 18z + (32x * -1 + 24y * -1 + -6z * -1) = 0 15x + -7y + 18z + (-32x + -24y + 6z) = 0 Reorder the terms: 15x + -32x + -7y + -24y + 18z + 6z = 0 Combine like terms: 15x + -32x = -17x -17x + -7y + -24y + 18z + 6z = 0 Combine like terms: -7y + -24y = -31y -17x + -31y + 18z + 6z = 0 Combine like terms: 18z + 6z = 24z -17x + -31y + 24z = 0 Solving -17x + -31y + 24z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31y' to each side of the equation. -17x + -31y + 31y + 24z = 0 + 31y Combine like terms: -31y + 31y = 0 -17x + 0 + 24z = 0 + 31y -17x + 24z = 0 + 31y Remove the zero: -17x + 24z = 31y Add '-24z' to each side of the equation. -17x + 24z + -24z = 31y + -24z Combine like terms: 24z + -24z = 0 -17x + 0 = 31y + -24z -17x = 31y + -24z Divide each side by '-17'. x = -1.823529412y + 1.411764706z Simplifying x = -1.823529412y + 1.411764706z
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