To solve the equation \( \sin(3x + 10°) = \cos(x + 24°) \), we can use the co-function identity:
\[ \sin(A) = \cos(90° - A) \]
We can set:
\[ 3x + 10° = 90° - (x + 24°) \]
Now simplify the right-hand side:
\[ 3x + 10° = 90° - x - 24° \] \[ 3x + 10° = 66° - x \]
Next, rearranging gives:
\[ 3x + x = 66° - 10° \] \[ 4x = 56° \] \[ x = \frac{56°}{4} = 14° \]
Now, we should check if this value of \( x \) fits within the acute angles of a right triangle, which is valid as \( 14° \) is an acute angle.
Thus, the value of \( x \) is:
\[ \boxed{14°} \]
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