Question

Write the algebraic inequality needed to solve the following problem, then show your solving steps and graph your solution set: Six more than one-fourth of a number is less than or equal to negative ten.

a) x/4+6≤−10
b) x/4−6≤−10
c) x/4+6≥−10
d) x/4−6≥−10

Answer 1

The algebraic inequality needed to solve the problem is x/4-6≥−10 (option d). To solve this inequality, add 6 to both sides, then multiply by 4. The solution set is x ≥ -16.

Step-by-step explanation:

The algebraic inequality needed to solve the problem is option d) x/4-6≥−10.

To solve this inequality, we can start by adding 6 to both sides of the inequality: x/4 - 6 + 6 ≥ -10 + 6. This simplifies to x/4 ≥ -4. Next, we can multiply both sides of the inequality by 4 to eliminate the fraction: 4 * x/4 ≥ -4 * 4, which simplifies to x ≥ -16. Therefore, the solution set is x ≥ -16.

To graph this solution set, we can draw a number line and shade the region to the right of -16 (including -16 as well since it is greater than or equal to), indicating that any value of x in that region satisfies the inequality.