Write 18z − 7 (−3 + 2z) in simplest form. select true or false for each statement.

the expression has 2 terms.
a true b false
the coefficient of z is 13.
a true b false
the constant is 21.

Simplest form = 4z + 21

Case 1: True, Case II: false and Case III: true

Step-by-step explanation:

18z - 7( -3 + 2z)

= 18z + 21 - 14z

= 18z -14z + 21

= 4z + 21

So, in the above expression we have two terms. First term is 4z and second term is 21.

So the first case is true. As the expression has two terms.

The coefficient of z is a number which is multiplied by z. Therefore, Second case is false as the coefficient of z is 4.

The constant is a number which is not multiplied by any variable. Therefore, third case is true as the constant number in above expression is 21.

there are no short passages to look at

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}