To solve the inequality [tex]\( 7x + 5y < -35 \)[/tex] for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the inequality. Let's go through the steps:
1. Start with the given inequality:
[tex]\[ 7x + 5y < -35 \][/tex]
2. Subtract [tex]\( 7x \)[/tex] from both sides of the inequality to isolate the term with [tex]\( y \)[/tex]:
[tex]\[ 5y < -35 - 7x \][/tex]
3. Divide every term in the inequality by 5 to solve for [tex]\( y \)[/tex]:
[tex]\[ y < \frac{-35 - 7x}{5} \][/tex]
4. Simplify the right-hand side:
[tex]\[
y < \frac{-35}{5} - \frac{7x}{5}
\][/tex]
[tex]\[
y < -7 - \frac{7x}{5}
\][/tex]
5. Rewrite the inequality in a more familiar form:
[tex]\[
y < -\frac{7x}{5} - 7
\][/tex]
In conclusion, the solution to the inequality [tex]\( 7x + 5y < -35 \)[/tex] is:
[tex]\[ y < -\frac{7x}{5} - 7 \][/tex]
