Question

-x-4>3x-2 (Solve the inequality)

Answer 1

First things first, collect like terms on either side:

\begin{align}
-x - 4 &> 3x - 2\\
-x &> 3x - 2 + 4\\
-x - 3x &> -2 + 4\\
-4x &> 2
\end{align}

Answer 2

Once we've done that, we can divide to get the x alone, but! When you divide by a negative and you have an inequality, you have to flip the direction of the inequality!

So:

\begin{align}
-4x &> 2\\
x &< -\frac{1}{2}
\end{align}

Answer 3

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Answer 4

Now, let's check it and make sure I didn't mess up. We'll try x = -1/2, which should *not* satisfy the inequality.

x = -1/2 means:

\begin{align}
-\frac{1}{2} - 4 &> 3\frac{-1}{2} - 2\\
-\frac{9}{2} &> -\frac{3}{2} - 2\\
-\frac{9}{2} &> -\frac{7}{2}
\end{align}

This isn't quite true, which is what we expect. Now let's try something less than -1/2, namely -1:

\begin{align}
-1 - 4 &> 3(-1) - 2\\
-5 &> -4 - 2\\
-5 &> -6
\end{align}

That's right! So it looks like the solution makes sense.

Answer 5

Yes. Solving inequalities is literally the same thing as solving a regular equation, except that when you multiply or divide by a negative, you have to flip the inequality sign.