Question

-2x+5+x is less than or equal to 3x+13

Answer 1

To solve the inequality \(-2x + 5 + x \leq 3x + 13\), follow these steps:

1. Combine like terms on the left side:
\[
-2x + x + 5 \leq 3x + 13
\]
This simplifies to:
\[
-x + 5 \leq 3x + 13
\]

2. Next, isolate the variable \(x\). Start by adding \(x\) to both sides:
\[
5 \leq 3x + x + 13
\]
Simplifying gives:
\[
5 \leq 4x + 13
\]

3. Now, subtract 13 from both sides:
\[
5 - 13 \leq 4x
\]
Which simplifies to:
\[
-8 \leq 4x
\]

4. Finally, divide both sides by 4:
\[
-2 \leq x
\]
This can also be written as:
\[
x \geq -2
\]

Thus, the solution to the inequality is:
\[
x \geq -2
\]