To solve the inequality [tex]\(-3x + 3 < 6\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Start with the given inequality:
[tex]\[
-3x + 3 < 6
\][/tex]
2. Subtract 3 from both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-3x + 3 - 3 < 6 - 3
\][/tex]
Simplifying the left and right sides gives:
[tex]\[
-3x < 3
\][/tex]
3. Divide both sides of the inequality by [tex]\(-3\)[/tex]. Remember, when you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality sign:
[tex]\[
\frac{-3x}{-3} > \frac{3}{-3}
\][/tex]
Simplifying this, we get:
[tex]\[
x > -1
\][/tex]
Thus, the solution to the inequality [tex]\(-3x + 3 < 6\)[/tex] is:
[tex]\[
x > -1
\][/tex]
