To determine the range of values for
x that satisfy the inequality
−5≤‌≤9, we start by solving each part of the compound inequality separately.
First, address
‌≥−5 :
Multiplying all terms by 4 (which is positive, so the inequality sign will not change), we get:
2−3x≥−20Now, adding
3x to both sides, we have:
2≥−20+3xNext, adding 20 to both sides gives:
22≥3xFinally, dividing both sides by 3 results in:
x≤‌Now, address
‌≤9 :
Again, multiplying all terms by 4 , we obtain:
2−3x≤36Next, subtracting 2 from each side:
−3x≤34Then, dividing both sides by -3 (and note that dividing by a negative number inverts the inequality sign):
x≥−‌Combining these two conditions, we obtain:
−‌≤x≤‌ However, we need to verify the results match the inequalities we derived. The compound inequality:
[−‌,‌]accurately reflects the comprehensive solution, which expresses the
x values between (and including)
−‌ and
‌‌. ‌Thus, the correct answer is:
Option D:
[−‌,‌]