To solve the inequality [tex]\( 2x < -x + 20 \)[/tex], we can follow these steps:
1. Isolate the variable [tex]\( x \)[/tex] on one side of the inequality:
To do this, we need to combine like terms. We start by adding [tex]\( x \)[/tex] to both sides of the inequality:
[tex]\[
2x + x < -x + 20 + x
\][/tex]
Simplifying the left and right sides, we have:
[tex]\[
3x < 20
\][/tex]
2. Solve for [tex]\( x \)[/tex] by dividing by the coefficient of [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the inequality by 3:
[tex]\[
x < \frac{20}{3}
\][/tex]
3. Determine the solution set:
Since there are no further restrictions or conditions given in the problem, the solution set is all [tex]\( x \)[/tex] such that [tex]\( x \)[/tex] is less than [tex]\(\frac{20}{3}\)[/tex].
In interval notation, the solution to the inequality [tex]\( 2x < -x + 20 \)[/tex] is:
[tex]\[
(-\infty, \frac{20}{3})
\][/tex]
This means that [tex]\( x \)[/tex] can be any real number less than [tex]\(\frac{20}{3}\)[/tex].
