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Simplifying 4[5 + -4(4 + -1t)] + -3 = 5[4(5t + -3) + 9] + -63 4[5 + (4 * -4 + -1t * -4)] + -3 = 5[4(5t + -3) + 9] + -63 4[5 + (-16 + 4t)] + -3 = 5[4(5t + -3) + 9] + -63 Combine like terms: 5 + -16 = -11 4[-11 + 4t] + -3 = 5[4(5t + -3) + 9] + -63 [-11 * 4 + 4t * 4] + -3 = 5[4(5t + -3) + 9] + -63 [-44 + 16t] + -3 = 5[4(5t + -3) + 9] + -63 Reorder the terms: -44 + -3 + 16t = 5[4(5t + -3) + 9] + -63 Combine like terms: -44 + -3 = -47 -47 + 16t = 5[4(5t + -3) + 9] + -63 Reorder the terms: -47 + 16t = 5[4(-3 + 5t) + 9] + -63 -47 + 16t = 5[(-3 * 4 + 5t * 4) + 9] + -63 -47 + 16t = 5[(-12 + 20t) + 9] + -63 Reorder the terms: -47 + 16t = 5[-12 + 9 + 20t] + -63 Combine like terms: -12 + 9 = -3 -47 + 16t = 5[-3 + 20t] + -63 -47 + 16t = [-3 * 5 + 20t * 5] + -63 -47 + 16t = [-15 + 100t] + -63 Reorder the terms: -47 + 16t = -15 + -63 + 100t Combine like terms: -15 + -63 = -78 -47 + 16t = -78 + 100t Solving -47 + 16t = -78 + 100t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-100t' to each side of the equation. -47 + 16t + -100t = -78 + 100t + -100t Combine like terms: 16t + -100t = -84t -47 + -84t = -78 + 100t + -100t Combine like terms: 100t + -100t = 0 -47 + -84t = -78 + 0 -47 + -84t = -78 Add '47' to each side of the equation. -47 + 47 + -84t = -78 + 47 Combine like terms: -47 + 47 = 0 0 + -84t = -78 + 47 -84t = -78 + 47 Combine like terms: -78 + 47 = -31 -84t = -31 Divide each side by '-84'. t = 0.369047619 Simplifying t = 0.369047619
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