Question

Three times the sum of a number and 20 is at least 15

Answer 1

The algebraic inequality for the statement 'three times the sum of a number and 20 is at least 15' is '3(x + 20) ≥ 15'. After solving, the unknown number 'x' must be greater than or equal to -15.

Step-by-step explanation:

To solve the problem statement, 'three times the sum of a number and 20 is at least 15', we begin by translating it into an algebraic inequality. This translates to '3(x + 20) ≥ 15', where 'x' represents the unknown number. To solve for 'x', we perform the following steps:

1. Expand the equation: 3(x + 20) = 3x + 60.
2. Set up the inequality: 3x + 60 ≥ 15.
3. Subtract 60 from both sides of the inequality: 3x ≥ 15 - 60, which simplifies to 3x ≥ -45.
4. Divide by 3 to isolate 'x': x ≥ -45 / 3.
5. Solve for 'x': x ≥ -15.

The solution to the inequality is that 'x' must be greater than or equal to -15.