Question

Two times the sum of some number y and 5 is less than or equal to 19 minus the product of 7 and the number. What inequality represents the possible values of y?

Answer 1

The inequality representing the possible values of y as stated in the word problem is y ≤ 1. This was derived by translating the problem into 2(y + 5) ≤ 19 - 7y and solving for y.

Step-by-step explanation:

The student is asked to translate a word problem into an inequality. The inequality represents the relationship 'Two times the sum of some number y and 5 is less than or equal to 19 minus the product of 7 and the number y'. This can be mathematically expressed as 2(y + 5) ≤ 19 - 7y. Now, let's solve for y:

1. Expand the left side of the inequality: 2y + 10 ≤ 19 - 7y.
2. Add 7y to both sides to get all y terms on one side: 2y + 7y + 10 ≤ 19.
3. Simplify by combining like terms: 9y + 10 ≤ 19.
4. Subtract 10 from both sides: 9y ≤ 9.
5. Divide both sides by 9: y ≤ 1.

The resulting inequality y ≤ 1 represents the possible values of y.