Sure, let's solve the inequality [tex]\(2x < -x + 20\)[/tex] step by step:
1. Combine like terms:
We start with the inequality:
[tex]\[
2x < -x + 20
\][/tex]
To combine the like terms, we need to add [tex]\(x\)[/tex] to both sides of the inequality. This gives us:
[tex]\[
2x + x < -x + x + 20
\][/tex]
Simplifying both sides, we get:
[tex]\[
3x < 20
\][/tex]
2. Isolate [tex]\(x\)[/tex]:
Now we need to solve for [tex]\(x\)[/tex] by isolating it on one side of the inequality. To do this, we divide both sides of the inequality by 3:
[tex]\[
\frac{3x}{3} < \frac{20}{3}
\][/tex]
This simplifies to:
[tex]\[
x < \frac{20}{3}
\][/tex]
3. Simplify the fraction:
The fraction [tex]\(\frac{20}{3}\)[/tex] can be converted to a decimal to understand it better:
[tex]\[
\frac{20}{3} \approx 6.666666666666667
\][/tex]
Therefore, the solution to the inequality [tex]\(2x < -x + 20\)[/tex] is [tex]\(x < 6.666666666666667\)[/tex].
