Final answer:
The equality 'Half of 7 added to product of h and 4 is at least 1' is translated into the algebraic inequality 3.5 + 4h ≥ 1. Solving for h, you get the solution h ≥ -0.625, meaning h can be any value greater than or equal to -0.625.
Step-by-step explanation:
The student's question is asking for the translation of a word problem into a mathematical inequality. The phrase 'Half of 7 added to the product of h and 4 is at least 1' can be expressed algebraically. To translate this, we can take 'half of 7' which is ½ × 7 or 3.5, then 'product of h and 4' which is 4h, and the phrase 'is at least 1' translates to ≥ 1. Putting this together, we get the inequality 3.5 + 4h ≥ 1.
To solve for h, we would subtract 3.5 from both sides of the inequality to isolate the term containing h, yielding the inequality 4h ≥ -2.5. Dividing both sides by 4 to solve for h gives us h ≥ -2.5/4, which simplifies to h ≥ -0.625. Therefore, any value of h that is greater than or equal to -0.625 satisfies the inequality.