Question 1104614
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The general solution for {{{sin(t) = 0.5}}} is {{{(pi/6)+2k(pi)}}} or {{{(5pi/6)+2k(pi)}}}.<br>
So you want to solve
(1) {{{(pi/4)(x-6) = (pi/6)+2k(pi)}}}
and
(2) {{{(pi/4)(x-6) = (5pi/6)+2k(pi)}}}<br>
Solving either one for x is basic algebra.  I'll do (1) and let you do (2)....<br>
{{{(pi/4)(x-6) = (pi/6)+2k(pi)}}}
{{{(pi/4)x-3pi/2 = pi/6+2k(pi)}}} [distribute...]
{{{(pi/4)x = 3pi/2+pi/6+2k(pi) = 5pi/3+2k(pi)}}}  [combine like terms...]
{{{(1/4)x = 5/3+2k}}}  [divide out the common factor "pi"]
{{{x = 20/3+8k}}}<br>
Any value of x of the form (20/3)+8k, where k is an integer, is a solution to the given equation.