-2x+5+x<3x+13

1 answer

To solve the inequality \(-2x + 5 + x < 3x + 13\), we can start by simplifying the left side.

Combine like terms on the left side:

\[ -2x + x = -x \]

So the inequality now looks like:

\[ -x + 5 < 3x + 13 \]

Next, let's get all the terms involving \(x\) on one side and the constant terms on the other. We can add \(x\) to both sides:

\[ 5 < 3x + x + 13 \]

Which simplifies to:

\[ 5 < 4x + 13 \]

Next, subtract \(13\) from both sides:

\[ 5 - 13 < 4x \]

This simplifies to:

\[ -8 < 4x \]

Now, divide both sides by \(4\):

\[ -\frac{8}{4} < x \]

Which simplifies to:

\[ -2 < x \]

Or we can write it as:

\[ x > -2 \]

Thus, the solution to the inequality is:

\[ \boxed{x > -2} \]