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Solve the inequality and represent your answer using set builder notation.

7-4x < 23
・{-4}
・{x : x < -4}
・4
・{x : x > -4}
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1 answer

To solve the inequality \( 7 - 4x < 23 \), we can follow these steps:

  1. Subtract 7 from both sides: \[ 7 - 4x - 7 < 23 - 7 \] This simplifies to: \[ -4x < 16 \]

  2. Divide both sides by -4: When we divide by a negative number, we must reverse the inequality sign. \[ x > \frac{16}{-4} \] Simplifying this gives: \[ x > -4 \]

  3. Represent the solution in set builder notation: The solution can be expressed as: \[ { x : x > -4 } \]

Thus, the answer is: \[ { x : x > -4 } \]