Final answer:
The inequality (4x + 6) / 7 > 7 cannot have a solution for x within the given constraints of x > -7 and x < 2 since the solution x > 10.75 does not meet the condition x < 2.
Step-by-step explanation:
To solve the inequality (4x + 6) / 7 > 7 for x, given the constraints that x > -7 and x < 2, we need to first isolate x on one side of the inequality:
- Multiply both sides by 7 to eliminate the fraction, which gives 4x + 6 > 49.
- Subtract 6 from both sides to get 4x > 43.
- Finally, divide both sides by 4 to solve for x, resulting in x > 10.75.
However, this solution does not fit within the given constraints of x > -7 and x < 2. Since 10.75 is not less than 2, there is no solution to this inequality within the provided constraints. We can use elimination and checking to confirm that the result is reasonable and aligns with the given values for x.