Final answer:
To solve the inequality 7 > x/4, multiply both sides by 4 to get 28 > x. This indicates that x must be less than 28, and checking this answer confirms it is reasonable.
Step-by-step explanation:
To solve the inequality 7 > \dfrac{x}{4}, we need to isolate the variable x. We start by eliminating terms where possible to simplify the algebra. To do this, we can multiply both sides of the inequality by 4, which is the denominator of the fraction. This step is allowed as long as we multiply all terms on both sides of the inequality by the same number.
The inequality then becomes 28 > x, which tells us that x must be less than 28 to satisfy the inequality. At this point, we have successfully isolated the variable. It is important to check the answer to ensure it is reasonable. Considering that 7 multiplied by 4 is indeed 28, we see that our manipulations of the inequality have retained its truth, which means our answer is reasonable.