Question

Solve the inequality and write your answer in interval notation.
1+6x>3(16x+9)

Answer 1

To solve the inequality \( 1 + 6x > 3(16x + 9) \), we first simplify the right-hand side.

1. Distribute the 3:
\[
1 + 6x > 48x + 27
\]

2. Next, we want to isolate \( x \) on one side. Start by subtracting \( 6x \) from both sides:
\[
1 > 48x - 6x + 27
\]
Simplifying further:
\[
1 > 42x + 27
\]

3. Now, subtract 27 from both sides:
\[
1 - 27 > 42x
\]
Simplifying the left-hand side:
\[
-26 > 42x
\]

4. Divide both sides by 42 (remember to reverse the inequality sign since we are dividing by a positive number):
\[
\frac{-26}{42} > x
\]
Simplifying \(\frac{-26}{42}\):
\[
\frac{-13}{21} > x
\]

Reversing the inequality gives us:
\[
x < \frac{-13}{21}
\]

In interval notation, the solution is:
\[
(-\infty, -\frac{13}{21})
\]