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Simplifying 7(t + -2) + 9(-3t + -6) = -21(t + 4) + 7 Reorder the terms: 7(-2 + t) + 9(-3t + -6) = -21(t + 4) + 7 (-2 * 7 + t * 7) + 9(-3t + -6) = -21(t + 4) + 7 (-14 + 7t) + 9(-3t + -6) = -21(t + 4) + 7 Reorder the terms: -14 + 7t + 9(-6 + -3t) = -21(t + 4) + 7 -14 + 7t + (-6 * 9 + -3t * 9) = -21(t + 4) + 7 -14 + 7t + (-54 + -27t) = -21(t + 4) + 7 Reorder the terms: -14 + -54 + 7t + -27t = -21(t + 4) + 7 Combine like terms: -14 + -54 = -68 -68 + 7t + -27t = -21(t + 4) + 7 Combine like terms: 7t + -27t = -20t -68 + -20t = -21(t + 4) + 7 Reorder the terms: -68 + -20t = -21(4 + t) + 7 -68 + -20t = (4 * -21 + t * -21) + 7 -68 + -20t = (-84 + -21t) + 7 Reorder the terms: -68 + -20t = -84 + 7 + -21t Combine like terms: -84 + 7 = -77 -68 + -20t = -77 + -21t Solving -68 + -20t = -77 + -21t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21t' to each side of the equation. -68 + -20t + 21t = -77 + -21t + 21t Combine like terms: -20t + 21t = 1t -68 + 1t = -77 + -21t + 21t Combine like terms: -21t + 21t = 0 -68 + 1t = -77 + 0 -68 + 1t = -77 Add '68' to each side of the equation. -68 + 68 + 1t = -77 + 68 Combine like terms: -68 + 68 = 0 0 + 1t = -77 + 68 1t = -77 + 68 Combine like terms: -77 + 68 = -9 1t = -9 Divide each side by '1'. t = -9 Simplifying t = -9
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