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Simplifying 3(2x + -6) + -4(3z + 1) = 5 + -2(z + 1) Reorder the terms: 3(-6 + 2x) + -4(3z + 1) = 5 + -2(z + 1) (-6 * 3 + 2x * 3) + -4(3z + 1) = 5 + -2(z + 1) (-18 + 6x) + -4(3z + 1) = 5 + -2(z + 1) Reorder the terms: -18 + 6x + -4(1 + 3z) = 5 + -2(z + 1) -18 + 6x + (1 * -4 + 3z * -4) = 5 + -2(z + 1) -18 + 6x + (-4 + -12z) = 5 + -2(z + 1) Reorder the terms: -18 + -4 + 6x + -12z = 5 + -2(z + 1) Combine like terms: -18 + -4 = -22 -22 + 6x + -12z = 5 + -2(z + 1) Reorder the terms: -22 + 6x + -12z = 5 + -2(1 + z) -22 + 6x + -12z = 5 + (1 * -2 + z * -2) -22 + 6x + -12z = 5 + (-2 + -2z) Combine like terms: 5 + -2 = 3 -22 + 6x + -12z = 3 + -2z Solving -22 + 6x + -12z = 3 + -2z Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 6x + 22 + -12z = 3 + 22 + -2z Reorder the terms: -22 + 22 + 6x + -12z = 3 + 22 + -2z Combine like terms: -22 + 22 = 0 0 + 6x + -12z = 3 + 22 + -2z 6x + -12z = 3 + 22 + -2z Combine like terms: 3 + 22 = 25 6x + -12z = 25 + -2z Add '12z' to each side of the equation. 6x + -12z + 12z = 25 + -2z + 12z Combine like terms: -12z + 12z = 0 6x + 0 = 25 + -2z + 12z 6x = 25 + -2z + 12z Combine like terms: -2z + 12z = 10z 6x = 25 + 10z Divide each side by '6'. x = 4.166666667 + 1.666666667z Simplifying x = 4.166666667 + 1.666666667z
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