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Simplifying 4(t + -6) + 6(-6t + -8) = -33(t + 2) + 1 Reorder the terms: 4(-6 + t) + 6(-6t + -8) = -33(t + 2) + 1 (-6 * 4 + t * 4) + 6(-6t + -8) = -33(t + 2) + 1 (-24 + 4t) + 6(-6t + -8) = -33(t + 2) + 1 Reorder the terms: -24 + 4t + 6(-8 + -6t) = -33(t + 2) + 1 -24 + 4t + (-8 * 6 + -6t * 6) = -33(t + 2) + 1 -24 + 4t + (-48 + -36t) = -33(t + 2) + 1 Reorder the terms: -24 + -48 + 4t + -36t = -33(t + 2) + 1 Combine like terms: -24 + -48 = -72 -72 + 4t + -36t = -33(t + 2) + 1 Combine like terms: 4t + -36t = -32t -72 + -32t = -33(t + 2) + 1 Reorder the terms: -72 + -32t = -33(2 + t) + 1 -72 + -32t = (2 * -33 + t * -33) + 1 -72 + -32t = (-66 + -33t) + 1 Reorder the terms: -72 + -32t = -66 + 1 + -33t Combine like terms: -66 + 1 = -65 -72 + -32t = -65 + -33t Solving -72 + -32t = -65 + -33t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '33t' to each side of the equation. -72 + -32t + 33t = -65 + -33t + 33t Combine like terms: -32t + 33t = 1t -72 + 1t = -65 + -33t + 33t Combine like terms: -33t + 33t = 0 -72 + 1t = -65 + 0 -72 + 1t = -65 Add '72' to each side of the equation. -72 + 72 + 1t = -65 + 72 Combine like terms: -72 + 72 = 0 0 + 1t = -65 + 72 1t = -65 + 72 Combine like terms: -65 + 72 = 7 1t = 7 Divide each side by '1'. t = 7 Simplifying t = 7
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