Final answer:
To solve the inequality 'twice the difference of a number and 7 is at most -17', the inequality 2(x - 7) ≤ -17 is formed and solved step by step, yielding the solution x ≤ -1.5.
Step-by-step explanation:
The student's question involves creating and solving an inequality from a word problem in mathematics. The phrase 'twice the difference of a number and 7 is at most -17' can be translated into the inequality 2(x - 7) ≤ -17. To solve for 'x', we can follow these steps:
Distribute the 2 into the parentheses: 2 * x - 2 * 7, which simplifies to 2x - 14.Next, we add 14 to both sides of the inequality to isolate the term with 'x' on one side: 2x - 14 + 14 ≤ -17 + 14. This simplifies to 2x ≤ -3.Finally, we divide both sides by 2 to solve for x: 2x / 2 ≤ -3 / 2, which gives us x ≤ -1.5.
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Therefore, the solution to the inequality is that the number 'x' can be any value less than or equal to -1.5.