For which value of x is the equation 3(3 + x) = 15 + x true?

x=3

Step-by-step explanation:

3(3 + x)=15+x

distribute

9 + 3x=  15+x

subtract x from each side

9+3x-x = 15

9+2x = 15

subtract 9 from each side

9+2x-9 = 15-9

2x = 6

divide by 2

2x/2 = 6/2

x=3

X = 3

Step-by-step explanation:

To solve for x, you can first divide both sides of the equation by 3. The reason you do this is because the left side is being multiplied by 3, so dividing would cancel it out

(3(3 + x) = 15 + x)/3   =  3 + x = 5 + 1/3x

Now, subtract 3 from both sides to isolate x on the left side

x = 2 + 1/3x

Lastly, subtract 1/3x from both sides

2/3x = 2

Now, divide both sides by 2/3 to get x = 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}