To solve the inequality [tex]\(-2x + 5 < 7\)[/tex], follow these steps:
1. Subtract 5 from both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-2x + 5 - 5 < 7 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
-2x < 2
\][/tex]
2. Divide both sides by -2. Remember that when you divide or multiply both sides of an inequality by a negative number, you must flip the direction of the inequality sign:
[tex]\[
\frac{-2x}{-2} > \frac{2}{-2}
\][/tex]
Simplifying this, we get:
[tex]\[
x > -1
\][/tex]
Therefore, the solution to the inequality [tex]\(-2x + 5 < 7\)[/tex] is:
[tex]\[
x > -1
\][/tex]
Among the given options, the correct answer is:
[tex]\[
x > -1
\][/tex]
