SOLUTION: What is the algebra domain of these two questions using algebraic sentence inequalities? 1. {{{ (3x-7)/(2x-3) }}} 2. {{{ square root of (7x+9) }}}

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Question 986279: What is the algebra domain of these two questions using algebraic sentence inequalities?
1. +%283x-7%29%2F%282x-3%29+

2. +square+root+of+%287x%2B9%29+
Answer by ikleyn(52799) About Me  (Show Source):
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1.  +%283x-7%29%2F%282x-3%29+.

      The domain is the entire number line  (all real numbers)  except of  x = 3%2F2,  where the denominator is zero.
      In terms of inequalities this set is the union of two semi-infinite intervals  x < 3%2F2  and  x > 3%2F2.

2.  sqrt%287x+%2B+9%29.

      The domain is the set of real numbers  x >= -9%2F7,  where the binom under the square root,  7x + 9,  is greater than or equal to zero:  7x + 9 >= 0.