42>-4x-6

Answer 1

To solve the inequality \( 42 > -4x - 6 \), you can follow these steps:

1. Add 6 to both sides to isolate the term with \( x \):

   \[ 42 + 6 > -4x \]

   This simplifies to:

   \[ 48 > -4x \]

   or

   \[ -4x < 48 \]

2. Divide both sides by -4. Remember that when you divide or multiply an inequality by a negative number, you must reverse the inequality sign:

   \[ x > \frac{48}{-4} \]

   Simplifying gives:

   \[ x > -12 \]

So the solution to the inequality is:

\[ x > -12 \]

In interval notation, this can be written as:

\[ (-12, \infty) \]