Certainly! Let's go through the steps to solve the inequality [tex]\( 4(4v + 6) < 9v + 3 \)[/tex] step by step:
1. Distribute the 4 on the left side of the inequality:
[tex]\[
4(4v + 6) < 9v + 3
\][/tex]
Distributing the 4, we get:
[tex]\[
4 \cdot 4v + 4 \cdot 6 < 9v + 3
\][/tex]
Simplifying further:
[tex]\[
16v + 24 < 9v + 3
\][/tex]
2. Move all terms involving [tex]\( v \)[/tex] to one side of the inequality:
To isolate [tex]\( v \)[/tex], subtract [tex]\( 9v \)[/tex] from both sides of the inequality:
[tex]\[
16v + 24 - 9v < 9v + 3 - 9v
\][/tex]
Simplifying this:
[tex]\[
7v + 24 < 3
\][/tex]
3. Move all constant terms to the other side of the inequality:
Subtract 24 from both sides:
[tex]\[
7v + 24 - 24 < 3 - 24
\][/tex]
Simplifying this:
[tex]\[
7v < -21
\][/tex]
4. Solve for [tex]\( v \)[/tex]:
Divide both sides by 7:
[tex]\[
v < \frac{-21}{7}
\][/tex]
Simplifying this:
[tex]\[
v < -3
\][/tex]
Therefore, the solution to the inequality [tex]\( 4(4v + 6) < 9v + 3 \)[/tex] is:
[tex]\[
v < -3
\][/tex]
