Question

Rewrite the double inequality in its basic form. 5<=x-4<=8

Answer 1

The double inequality 5≤x-4≤8 is rewritten in its basic form by adding 4 to each part, resulting in the simple inequality 9≤x≤12.

Step-by-step explanation:

The student's question asks to rewrite the double inequality 5≤x-4≤8 in its basic form. To do so, we need to isolate the variable x in the middle of the inequality. We achieve this by performing the same operation on all three parts of the inequality, which in this case is adding 4 to each part. Here is the step-by-step breakdown:

1. Add 4 to all three parts: 5 + 4 ≤ x - 4 + 4 ≤ 8 + 4
2. Simplify: 9 ≤ x ≤ 12

Now we have the inequality in its basic form, indicating that x is a number between 9 and 12, inclusive.