Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number?
Let x = the number. Notice that quotient is a key word for division, and at least means greater than or equal to. From the question, the sentence would translate to: x + 5 ≥ x. Subtract 5 from both sides of the inequality: x/2 + 5 - 5 ≥ x - 5; simplify: x/2 ≥ x - 5. Multiply both sides of x the inequality through 2: x/2 × 2 ≥ (x - 5) × 2; simplify: x ≥ (x - 5)2. Use the distributive property on the right side of the inequality: x ≥ 2x - 10. Add 10 to both sides of the inequality: x + 10 ≥ 2x - 10 + 10; simplify: x + 10 ≥ 2x. Subtract x from both sides of the inequality: x - x + 10 ≥ 2x - x.
The variable is now alone: 10 ≥ x. The number is at most 10.