Question

Twice the sum of a number and 9 is no more

than 3 times the same number increased by
15. Solve the inequality and graph the solu-
tion set.

Answer 1

To solve the inequality 2(x + 9) ≤ 3x + 15, distribute the 2, subtract 2x and 15 from both sides to isolate the variable, giving x ≥ 3. The graph of this solution is a solid dot at 3 with the shading to the right, representing all numbers greater than or equal to 3.

Step-by-step explanation:

The student is asking to solve the inequality: 2(x + 9) ≤ 3x + 15, where 'x' represents the number in question. First, distribute the 2 in the left-hand side of the inequality:

2x + 18 ≤ 3x + 15

Next, move all variables to one side and constants to the other by subtracting 2x from both sides and subtracting 15 from both sides:

18 ≤ x + 15

Then subtract 15 from both sides:

3 ≤ x

This means that the solution to the inequality is x ≥ 3. To graph this solution on a number line, make a solid dot at 3 and shade to the right, indicating all numbers greater than or equal to 3 are part of the solution set.