-6.2 - 12.6x = 5.8 - 7.8x

x = -2.5

Step-by-step explanation:

Step 1: Write equation

-6.2 - 12.6x = 5.8 - 7.8x

Step 2: Solve for x

Add 12.6x on both sides: -6.2 = 5.8 + 4.8x

Subtract 5.8 on both sides: -12 = 4.8x

Divide both sides by 4.8: x = -2.5

Step 3: Check

Plug in x to verify if it's a solution.

-6.2 - 12.6(-2.5) = 5.8 - 7.8(-2.5)

-6.2 + 31.5 = 5.8 + 19.5

25.3 = 25.3

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}