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Simplifying -6(t + 1) + -1t + -10 = 7(t + 4) + 12 Reorder the terms: -6(1 + t) + -1t + -10 = 7(t + 4) + 12 (1 * -6 + t * -6) + -1t + -10 = 7(t + 4) + 12 (-6 + -6t) + -1t + -10 = 7(t + 4) + 12 Reorder the terms: -6 + -10 + -6t + -1t = 7(t + 4) + 12 Combine like terms: -6 + -10 = -16 -16 + -6t + -1t = 7(t + 4) + 12 Combine like terms: -6t + -1t = -7t -16 + -7t = 7(t + 4) + 12 Reorder the terms: -16 + -7t = 7(4 + t) + 12 -16 + -7t = (4 * 7 + t * 7) + 12 -16 + -7t = (28 + 7t) + 12 Reorder the terms: -16 + -7t = 28 + 12 + 7t Combine like terms: 28 + 12 = 40 -16 + -7t = 40 + 7t Solving -16 + -7t = 40 + 7t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7t' to each side of the equation. -16 + -7t + -7t = 40 + 7t + -7t Combine like terms: -7t + -7t = -14t -16 + -14t = 40 + 7t + -7t Combine like terms: 7t + -7t = 0 -16 + -14t = 40 + 0 -16 + -14t = 40 Add '16' to each side of the equation. -16 + 16 + -14t = 40 + 16 Combine like terms: -16 + 16 = 0 0 + -14t = 40 + 16 -14t = 40 + 16 Combine like terms: 40 + 16 = 56 -14t = 56 Divide each side by '-14'. t = -4 Simplifying t = -4
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