2(2x-8)-8x underlined< 0

Answer 1

To solve the inequality \( 2(2x - 8) - 8x < 0 \), let's simplify it step-by-step.

1. Distribute the \(2\) in the expression:

\[ 2(2x) - 2(8) - 8x < 0 \] \[ 4x - 16 - 8x < 0 \]

2. Combine like terms:

\[ 4x - 8x - 16 < 0 \] \[ -4x - 16 < 0 \]

3. Add \(16\) to both sides:

\[ -4x < 16 \]

4. Divide by \(-4\), remembering to reverse the inequality sign:

\[ x > -4 \]

Thus, the solution to the inequality \(2(2x - 8) - 8x < 0\) is

\[ x > -4 \]

This means that \(x\) can take any value greater than \(-4\).