Question

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

Answer 1

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:

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