Let's solve the inequality step by step.

Given inequality: $8(6x + 5) + 2 \ge 2x + 7$

Step 1: Distribute the 8 on the left-hand side.

$8 \times 6x + 8 \times 5 + 2 \ge 2x + 7$ $48x + 40 + 2 \ge 2x + 7$

Step 2: Combine like terms on the left-hand side.

$48x + 42 \ge 2x + 7$

Step 3: Subtract $2x$ from both sides to move the terms involving $x$ to one side.

$48x - 2x + 42 \ge 7$ $46x + 42 \ge 7$

Step 4: Subtract 42 from both sides to isolate the term with $x$.

$46x \ge 7 - 42$ $46x \ge -35$

Step 5: Divide both sides by 46 to solve for $x$.

$x \ge \frac{-35}{46}$

Step 6: Simplify the fraction if possible.

$x \ge \frac{-35}{46}$ The fraction $\frac{-35}{46}$ cannot be simplified further, so the solution is: $x \ge \frac{-35}{46}$

This is the final answer.

Would you like further details on this solution, or do you have any questions?

Related Questions:

1. How do you solve inequalities involving distribution?
2. What happens if you multiply or divide both sides of an inequality by a negative number?
3. How can you graph the solution of an inequality on a number line?
4. What are the rules for combining like terms in algebraic expressions?
5. How does the solution change if the inequality sign is reversed?

Tip:

When solving inequalities, always remember to flip the inequality sign if you multiply or divide both sides by a negative number.