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Simplifying 1.3(z + -0.7) + -0.12(z + 10) = 5z + -9.75 Reorder the terms: 1.3(-0.7 + z) + -0.12(z + 10) = 5z + -9.75 (-0.7 * 1.3 + z * 1.3) + -0.12(z + 10) = 5z + -9.75 (-0.91 + 1.3z) + -0.12(z + 10) = 5z + -9.75 Reorder the terms: -0.91 + 1.3z + -0.12(10 + z) = 5z + -9.75 -0.91 + 1.3z + (10 * -0.12 + z * -0.12) = 5z + -9.75 -0.91 + 1.3z + (-1.2 + -0.12z) = 5z + -9.75 Reorder the terms: -0.91 + -1.2 + 1.3z + -0.12z = 5z + -9.75 Combine like terms: -0.91 + -1.2 = -2.11 -2.11 + 1.3z + -0.12z = 5z + -9.75 Combine like terms: 1.3z + -0.12z = 1.18z -2.11 + 1.18z = 5z + -9.75 Reorder the terms: -2.11 + 1.18z = -9.75 + 5z Solving -2.11 + 1.18z = -9.75 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -2.11 + 1.18z + -5z = -9.75 + 5z + -5z Combine like terms: 1.18z + -5z = -3.82z -2.11 + -3.82z = -9.75 + 5z + -5z Combine like terms: 5z + -5z = 0 -2.11 + -3.82z = -9.75 + 0 -2.11 + -3.82z = -9.75 Add '2.11' to each side of the equation. -2.11 + 2.11 + -3.82z = -9.75 + 2.11 Combine like terms: -2.11 + 2.11 = 0.00 0.00 + -3.82z = -9.75 + 2.11 -3.82z = -9.75 + 2.11 Combine like terms: -9.75 + 2.11 = -7.64 -3.82z = -7.64 Divide each side by '-3.82'. z = 2 Simplifying z = 2
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