What is the answer for the equation 4|x+1/3|=20 ? a. x=411/12or-411/12 b. x=411/12 c. x=42/3or-51/3d. no solution

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Selection C is appropriate.

Divide by 4, unfold, subtract 1/3.
.. |x +1/3| = 5
.. -5 = x +1/3 . . . . one choice for the sign of the content of |x +1/3|
.. -5 1/3 = x

.. x +1/3 = 5 . . . . the other choice
.. x = 4 2/3

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If this were an inequality |x +1/3| < 5, I would "unfold" it as
.. -5 < x +1/3 < 5 . . . . . . . copy the right side expression to the left with reversed sign.
The above is an approximation of that. You can't really write -5 = ( ) = 5, because it is a gross violation of the equal sign. But you can write the two versions:
.. -5 = ( )
.. ( ) = 5

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12