Questions: 3x+5<6 or 8x-2>10

Solution Steps

To solve the given inequalities, we need to isolate the variable \( x \) in each inequality separately. Then, we will find the union of the solution sets for both inequalities.

To solve the inequality \(3x + 5 < 6\), we first isolate \(x\):

\[ 3x + 5 < 6 \]

Subtract 5 from both sides:

\[ 3x < 1 \]

Divide by 3:

\[ x < \frac{1}{3} \]

To solve the inequality \(8x - 2 > 10\), we first isolate \(x\):

\[ 8x - 2 > 10 \]

Add 2 to both sides:

\[ 8x > 12 \]

Divide by 8:

\[ x > \frac{3}{2} \]

The solution to the original problem is the union of the solution sets for both inequalities:

\[ x < \frac{1}{3} \quad \text{or} \quad x > \frac{3}{2} \]

Final Answer