If pr = 40, what are pq and qr?

the image consists of a segment pr and point q is between points p and r. measure of segment pq is 5x-2 and that of segment qr is x+12.

a. pq = 8, qr = 17
b. pq = 23, qr = 17
c. pq = 27, qr = 13
d. pq = 19, qr = 21

B. PQ = 23, QR = 17

Step-by-step explanation:

Given,

In segment PR,

Q is the point between points P and R,

That is, PR = PQ + QR,

We have, PR = 40 unit, PQ = 5x - 2 and QR = x + 12,

By substituting the values,

40 = 5x - 2 + x + 12

40 = 6x + 10

30 = 6x

⇒ x = 5

Hence, PQ = 5(5) - 2 = 25 - 2 = 23 unit,

And, QR = 5 + 12 = 17 unit

OPTION B is correct

answer: c i think

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.