Solve |x-3|=7 plz help asap I will mark brainliest

x=10  or x=-4

Step-by-step explanation:

|x-3|=7

There are two solutions, one positive and one negative

x-3 = 7   and x-3 = -7

Add 3 to all sides

x-3+3 = 7+3           x-3+3 = -7+3

x = 10                    x = -4

Well, if we are taking the absolute value, of |x - 3| = 7, then you have a total of two cases. 7 can be either positive or negitive.

Knowing this, we can write out our two cases as:

|x - 3| = 7, or

|x - 3| = -7

Using these two equations, we can solve the equations for our values of x:

First Case:

|x - 3| = 7

x - 3 = 7

x = 10

Second Case:

|x - 3| = -7

x - 3 = -7

x = -4

So, our two cases show us that x can equal -4, or 10.

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

step-by-step explanation:

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