Question

Slovenia the equation for x: (cuberoute4) 2x+1/2=1/32.

Answer 1

cube root of 4 = 41/3
(cube root of 4)2x + 1/2 = 41/3 ( 2x + 1/2) = 4 1/3 [( 4x + 1 ) / 2 ] = 4 (4x + 1) / 6


Since 4 = 22

4 (4x + 1) / 6 = 2 2 (4x + 1) / 6 = 2 (4x + 1) / 3

Now, 1 / 32 = 1 / 25

This is in the form 1/ am which is a -m

2 (4x + 1) / 3 = 2 -5

Since it is 2 on both sides, we now take the exponents.

(4x + 1) / 3 = -5
(4x + 1) = -15
4x = -15 - 1 = -16
x = -16 / 4 = -4

HENCE, X = -4

For verification

2 (4x + 1) / 3 = 2 [(4 * -4) + 1] / 3 = 2 -15 / 3 = 2-5 which is RHS

Therefore, LHS = RHS