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Simplifying 12x + 13y + 45z = 24x + -15y + 35z Solving 12x + 13y + 45z = 24x + -15y + 35z Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24x' to each side of the equation. 12x + 13y + -24x + 45z = 24x + -15y + -24x + 35z Reorder the terms: 12x + -24x + 13y + 45z = 24x + -15y + -24x + 35z Combine like terms: 12x + -24x = -12x -12x + 13y + 45z = 24x + -15y + -24x + 35z Reorder the terms: -12x + 13y + 45z = 24x + -24x + -15y + 35z Combine like terms: 24x + -24x = 0 -12x + 13y + 45z = 0 + -15y + 35z -12x + 13y + 45z = -15y + 35z Add '-13y' to each side of the equation. -12x + 13y + -13y + 45z = -15y + -13y + 35z Combine like terms: 13y + -13y = 0 -12x + 0 + 45z = -15y + -13y + 35z -12x + 45z = -15y + -13y + 35z Combine like terms: -15y + -13y = -28y -12x + 45z = -28y + 35z Add '-45z' to each side of the equation. -12x + 45z + -45z = -28y + 35z + -45z Combine like terms: 45z + -45z = 0 -12x + 0 = -28y + 35z + -45z -12x = -28y + 35z + -45z Combine like terms: 35z + -45z = -10z -12x = -28y + -10z Divide each side by '-12'. x = 2.333333333y + 0.8333333333z Simplifying x = 2.333333333y + 0.8333333333z
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