# Solve absolute value equations and show work step by step please due tomorrow

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Answer:12) x = 10 or x = -1013) b = 3 or b = -3.14) r = 6 or r = -2 15) n = 0 or -2Step-by-step explanation:12) Given, 4|x| + 3 = 43 Now, for x ≥ 0, |x| = x and for x < 0, |x| = -x So, for x ≥ 0, the equation becomes 4x + 3 = 43 ⇒ 4x = 40 ⇒ x = 10 Again, for x < 0, we have - 4x + 3 = 43 ⇒ - 4x = 40 ⇒ x = - 10 Therefore, the solution of the equation is x = 10 or x = -10. (Answer) 13) Given, 3|b| + 5 = 14 Now, for b ≥ 0, |b| = b and for b < 0, |b| = -b So, for b ≥ 0, the equation becomes 3b + 5 = 14 ⇒ 3b = 9 ⇒ b = 3 Again, for b < 0, we have - 3b + 5 = 14 ⇒ - 3b = 9 ⇒ b = - 3 Therefore, the solution of the equation is b = 3 or b = -3. (Answer) 14) 9|2r - 4| + 1 = 73 Now, for 2r - 4 ≥0 i.e. r ≥ 2, then 9(2r - 4) + 1 = 73 ⇒ 2r - 4 = 8 ⇒ 2r = 12 ⇒ r = 6 Again, for (2r - 4) < 0 i.e. r < 2, then 9(4 - 2r) + 1 = 73 ⇒ 4 - 2r = 8 ⇒ 2r = - 4 ⇒ r = -2 Hence, the solutions are r = 6 and r = -2 (Answer) 15) For, 10n + 10 ≥ 0 i.e. n ≥ -1, then 1 + 4(10n + 10) = 41 ⇒ 10n + 10 =10 ⇒ 10n = 0 ⇒ n = 0 Again, for 10n + 10 < 0 i.e. n < -1, then 1 - 4(10n + 10) = 41 ⇒ 10n + 10 = - 10 ⇒ 10n = -20 ⇒ n = -2 Hence, the solution is n = 0 or -2 (Answer)