X − (5 − 3x) ≤ 2x − 1 Group of answer choices Number line with a filled circle at -1 and shading to the left Number line with a filled circle at -1 and shading to the right Number line with a filled circle at 2 and shading to the right Number line with a filled circle at 2 and shading to the left

Given:

The inequality is

To find:

The solution of the given inequality.

Solution:

We have,

Subtract 2x from both sides.

Add 5 on both sides.

Divide both sides by 2.

It means, the numbers less than 2 or 2 are included in the solution set.

Number on the left side of 2 are less than 2. So, number line with a filled circle at 2 and shading to the left.

Therefore, the correct option is D.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt