Question

Solve the inequities.
5 + 5x < 35 or 2x -4 /leq -14

Answer 1

To solve the inequalities \(5 + 5x < 35\) and \(2x - 4 \leq -14\), we will solve each inequality separately.

1. **First Inequality**:
\[
5 + 5x < 35
\]
Subtract 5 from both sides:
\[
5x < 30
\]
Now, divide both sides by 5:
\[
x < 6
\]

2. **Second Inequality**:
\[
2x - 4 \leq -14
\]
Add 4 to both sides:
\[
2x \leq -10
\]
Now, divide both sides by 2:
\[
x \leq -5
\]

Now, we combine the results of the two inequalities:
- From the first inequality, we have \(x < 6\).
- From the second inequality, we have \(x \leq -5\).

Since we are looking for the union of the two inequalities (\( \text{or} \)), the final solution is:
\[
x < 6 \quad \text{or} \quad x \leq -5
\]

In interval notation, the solution is:
\[
(-\infty, -5] \cup (-\infty, 6)
\]

Thus, the complete solution is:
\[
x < 6 \quad \text{or} \quad x \leq -5
\]