What expression is equivalent to: 3x-4(y+3)-10+8x?

-4 y + 11 x + -22

Step-by-step explanation:

Simplify the following:

3 x - 4 (y + 3) - 10 + 8 x

Hint: | Group like terms in 3 x - 4 (y + 3) - 10 + 8 x.

Grouping like terms, 3 x - 4 (y + 3) - 10 + 8 x = -4 (y + 3) + (3 x + 8 x) - 10:

-4 (y + 3) + (3 x + 8 x) - 10

Hint: | Add like terms in 3 x + 8 x.

3 x + 8 x = 11 x:

-4 (y + 3) + 11 x - 10

Hint: | Distribute -4 over y + 3.

-4 (y + 3) = -4 y - 12:

-4 y - 12 + 11 x - 10

Hint: | Group like terms in -4 y + 11 x - 12 - 10.

Grouping like terms, -4 y + 11 x - 12 - 10 = -4 y + 11 x + (-12 - 10):

-4 y + 11 x + (-12 - 10)

Hint: | Evaluate -12 - 10.

-12 - 10 = -22:

 -4 y + 11 x + -22

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}

answer is x<