Question

Consider the following inequality:2(- 4x + 4) > - 8x + 6Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.AnswerKeypadKeyboard ShortcutsIf all real numbers satisfy the inequality, select All Real Numbers. If no real number satisfies the inequality,select No SolutionSelecting one of the alternative options will replace the entered value(s) with the selected value. Otherwise,the entered answer is used,O No SolutionO All Real Numbers

Answer 1

To solve this inequality, we can proceed as follows:

1. Apply the distributive property at the left side of the inequality:

`\begin{gathered} 2(-4x+4)>-8x+6 \\ 2(-4x)+2(4)>-8x+6 \\ -8x+8>-8x+6 \end{gathered}`

2. We can add 8x to both sides of the inequality:

`\begin{gathered} -8x+8x+8>-8x+8x+6 \\ 8>6 \end{gathered}`

And we obtain that 8 > 6. This is always true. Therefore, we can say that all the real numbers satisfy the inequality, and we can select All Real Numbers.

In summary, all real numbers satisfy the inequality. Then the answer is All Real Numbers.