To determine which inequality is equivalent to [tex]\(-3x - 5y < 4y - 6\)[/tex], follow these steps:
1. Start with the original inequality:
[tex]\[
-3x - 5y < 4y - 6
\][/tex]
2. Move all the terms involving [tex]\(y\)[/tex] to the right side:
[tex]\[
-3x < 4y - 6 + 5y
\][/tex]
3. Combine like terms on the right side:
[tex]\[
-3x < 9y - 6
\][/tex]
4. Isolate [tex]\(x\)[/tex] by dividing both sides by -3. Remember, when you divide both sides of an inequality by a negative number, the inequality sign flips.
[tex]\[
x > \frac{9y - 6}{-3}
\][/tex]
5. Simplify the right side of the inequality:
[tex]\[
x > -3y + 2
\][/tex]
Thus, the inequality that is equivalent to the original expression [tex]\(-3x - 5y < 4y - 6\)[/tex] is:
[tex]\[
x > -3y + 2
\][/tex]
Among the given options, the correct inequality is:
B) [tex]\(x > -3y + 2\)[/tex]
