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Simplifying -13(5y + -15) = 17 + 19(-9y + -6) + -13(-11y + 11) Reorder the terms: -13(-15 + 5y) = 17 + 19(-9y + -6) + -13(-11y + 11) (-15 * -13 + 5y * -13) = 17 + 19(-9y + -6) + -13(-11y + 11) (195 + -65y) = 17 + 19(-9y + -6) + -13(-11y + 11) Reorder the terms: 195 + -65y = 17 + 19(-6 + -9y) + -13(-11y + 11) 195 + -65y = 17 + (-6 * 19 + -9y * 19) + -13(-11y + 11) 195 + -65y = 17 + (-114 + -171y) + -13(-11y + 11) Reorder the terms: 195 + -65y = 17 + -114 + -171y + -13(11 + -11y) 195 + -65y = 17 + -114 + -171y + (11 * -13 + -11y * -13) 195 + -65y = 17 + -114 + -171y + (-143 + 143y) Reorder the terms: 195 + -65y = 17 + -114 + -143 + -171y + 143y Combine like terms: 17 + -114 = -97 195 + -65y = -97 + -143 + -171y + 143y Combine like terms: -97 + -143 = -240 195 + -65y = -240 + -171y + 143y Combine like terms: -171y + 143y = -28y 195 + -65y = -240 + -28y Solving 195 + -65y = -240 + -28y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '28y' to each side of the equation. 195 + -65y + 28y = -240 + -28y + 28y Combine like terms: -65y + 28y = -37y 195 + -37y = -240 + -28y + 28y Combine like terms: -28y + 28y = 0 195 + -37y = -240 + 0 195 + -37y = -240 Add '-195' to each side of the equation. 195 + -195 + -37y = -240 + -195 Combine like terms: 195 + -195 = 0 0 + -37y = -240 + -195 -37y = -240 + -195 Combine like terms: -240 + -195 = -435 -37y = -435 Divide each side by '-37'. y = 11.75675676 Simplifying y = 11.75675676
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