What is 8(y-5) = 6y-18

y = 11

Explanation:

8(y − 5) = 6y − 18

Simplify both sides of the equation

8(y − 5) = 6y − 18

(8)(y) + (8)(−5) = 6y + −18( Distribute)

8y + −40 = 6y + −18

8y − 40 = 6y − 18

Subtract 6y from both sides

8y − 40 − 6y = 6y − 18 − 6y

2y − 40 = −18

Add 40 to both sides

2y − 40 + 40 = −18 + 40

2y = 22

Step 4: Divide both sides by 2

2y / 2 = 22 / 2

y = 11

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}