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Simplifying 250 + -1r + 48s + -2(41 + -1r(s + -24)) = 195r + 4(s + -2r(21 + -4s)) Reorder the terms: 250 + -1r + 48s + -2(41 + -1r(-24 + s)) = 195r + 4(s + -2r(21 + -4s)) 250 + -1r + 48s + -2(41 + (-24 * -1r + s * -1r)) = 195r + 4(s + -2r(21 + -4s)) 250 + -1r + 48s + -2(41 + (24r + -1rs)) = 195r + 4(s + -2r(21 + -4s)) 250 + -1r + 48s + (41 * -2 + 24r * -2 + -1rs * -2) = 195r + 4(s + -2r(21 + -4s)) 250 + -1r + 48s + (-82 + -48r + 2rs) = 195r + 4(s + -2r(21 + -4s)) Reorder the terms: 250 + -82 + -1r + -48r + 2rs + 48s = 195r + 4(s + -2r(21 + -4s)) Combine like terms: 250 + -82 = 168 168 + -1r + -48r + 2rs + 48s = 195r + 4(s + -2r(21 + -4s)) Combine like terms: -1r + -48r = -49r 168 + -49r + 2rs + 48s = 195r + 4(s + -2r(21 + -4s)) 168 + -49r + 2rs + 48s = 195r + 4(s + (21 * -2r + -4s * -2r)) 168 + -49r + 2rs + 48s = 195r + 4(s + (-42r + 8rs)) Reorder the terms: 168 + -49r + 2rs + 48s = 195r + 4(-42r + 8rs + s) 168 + -49r + 2rs + 48s = 195r + (-42r * 4 + 8rs * 4 + s * 4) 168 + -49r + 2rs + 48s = 195r + (-168r + 32rs + 4s) Combine like terms: 195r + -168r = 27r 168 + -49r + 2rs + 48s = 27r + 32rs + 4s Solving 168 + -49r + 2rs + 48s = 27r + 32rs + 4s Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-27r' to each side of the equation. 168 + -49r + 2rs + -27r + 48s = 27r + 32rs + -27r + 4s Reorder the terms: 168 + -49r + -27r + 2rs + 48s = 27r + 32rs + -27r + 4s Combine like terms: -49r + -27r = -76r 168 + -76r + 2rs + 48s = 27r + 32rs + -27r + 4s Reorder the terms: 168 + -76r + 2rs + 48s = 27r + -27r + 32rs + 4s Combine like terms: 27r + -27r = 0 168 + -76r + 2rs + 48s = 0 + 32rs + 4s 168 + -76r + 2rs + 48s = 32rs + 4s Add '-32rs' to each side of the equation. 168 + -76r + 2rs + -32rs + 48s = 32rs + -32rs + 4s Combine like terms: 2rs + -32rs = -30rs 168 + -76r + -30rs + 48s = 32rs + -32rs + 4s Combine like terms: 32rs + -32rs = 0 168 + -76r + -30rs + 48s = 0 + 4s 168 + -76r + -30rs + 48s = 4s Add '-168' to each side of the equation. 168 + -76r + -30rs + -168 + 48s = -168 + 4s Reorder the terms: 168 + -168 + -76r + -30rs + 48s = -168 + 4s Combine like terms: 168 + -168 = 0 0 + -76r + -30rs + 48s = -168 + 4s -76r + -30rs + 48s = -168 + 4s Add '-48s' to each side of the equation. -76r + -30rs + 48s + -48s = -168 + 4s + -48s Combine like terms: 48s + -48s = 0 -76r + -30rs + 0 = -168 + 4s + -48s -76r + -30rs = -168 + 4s + -48s Combine like terms: 4s + -48s = -44s -76r + -30rs = -168 + -44s Reorder the terms: 168 + -76r + -30rs + 44s = -168 + -44s + 168 + 44s Reorder the terms: 168 + -76r + -30rs + 44s = -168 + 168 + -44s + 44s Combine like terms: -168 + 168 = 0 168 + -76r + -30rs + 44s = 0 + -44s + 44s 168 + -76r + -30rs + 44s = -44s + 44s Combine like terms: -44s + 44s = 0 168 + -76r + -30rs + 44s = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(84 + -38r + -15rs + 22s) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(84 + -38r + -15rs + 22s)' equal to zero and attempt to solve: Simplifying 84 + -38r + -15rs + 22s = 0 Solving 84 + -38r + -15rs + 22s = 0 Move all terms containing r to the left, all other terms to the right. Add '-84' to each side of the equation. 84 + -38r + -15rs + -84 + 22s = 0 + -84 Reorder the terms: 84 + -84 + -38r + -15rs + 22s = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -38r + -15rs + 22s = 0 + -84 -38r + -15rs + 22s = 0 + -84 Combine like terms: 0 + -84 = -84 -38r + -15rs + 22s = -84 Add '-22s' to each side of the equation. -38r + -15rs + 22s + -22s = -84 + -22s Combine like terms: 22s + -22s = 0 -38r + -15rs + 0 = -84 + -22s -38r + -15rs = -84 + -22s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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