Answer:
12) x = 10 or x = -10
13) b = 3 or b = -3.
14) r = 6 or r = -2
15) n = 0 or -2
Step-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)
