Sure, let's solve the inequality [tex]\(2x < -x + 20\)[/tex] step by step.
1. Isolate the variable x on one side:
To begin, we want to move all terms involving [tex]\(x\)[/tex] to the same side of the inequality. Currently, the inequality is:
[tex]\[
2x < -x + 20
\][/tex]
To do this, add [tex]\(x\)[/tex] to both sides of the inequality:
[tex]\[
2x + x < -x + x + 20
\][/tex]
Simplifying this, we get:
[tex]\[
3x < 20
\][/tex]
2. Solve for x:
Now we need to isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by 3:
[tex]\[
x < \frac{20}{3}
\][/tex]
Simplifying the fraction:
[tex]\[
x < 6.67
\][/tex]
So, the solution to the inequality [tex]\(2x < -x + 20\)[/tex] is:
[tex]\[
x < 6.67
\][/tex]
