The best first step in solving the inequality [tex]\( -4x + \frac{2}{5} > \frac{5}{10} \)[/tex] is:
Subtract [tex]\(\frac{2}{5}\)[/tex] from both sides.
Let's work through the inequality step by step:
1. Start with the given inequality:
[tex]\[
-4x + \frac{2}{5} > \frac{5}{10}
\][/tex]
2. Subtract [tex]\(\frac{2}{5}\)[/tex] from both sides of the inequality. This helps isolate the term involving [tex]\( x \)[/tex] on one side:
[tex]\[
-4x + \frac{2}{5} - \frac{2}{5} > \frac{5}{10} - \frac{2}{5}
\][/tex]
3. Simplify the terms on both sides. On the left side, [tex]\(\frac{2}{5} - \frac{2}{5} = 0\)[/tex], so you are left with:
[tex]\[
-4x > \frac{5}{10} - \frac{2}{5}
\][/tex]
4. Convert [tex]\(\frac{2}{5}\)[/tex] to have the same denominator as [tex]\(\frac{5}{10}\)[/tex]:
[tex]\[
\frac{2}{5} = \frac{4}{10}
\][/tex]
5. Now subtract the fractions on the right side:
[tex]\[
-4x > \frac{5}{10} - \frac{4}{10}
\][/tex]
6. Simplify the right side:
[tex]\[
-4x > \frac{1}{10}
\][/tex]
So the inequality now is [tex]\( -4x > \frac{1}{10} \)[/tex].
Thus, subtracting [tex]\(\frac{2}{5}\)[/tex] from both sides is the best first step to solve the inequality.
