Question

I have 4 questions

1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units, then what is TV? 131 194 68 80

2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x? x = 3 x = 7 x = 12.5 x = 22

3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?

4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?

Answer 1

1.
`TV = 68`

2.
`x = 7`

3.
`x = 21`

4.
`CD = 8`

Explanation:

Solving (1):

Given

`RT = 63`

`RV = 131`

Required

Determine TV

To solve TV, we make use of the following formula;

`RV = RT + TV`

Substitute values for RT and RV

`131 = 63 + TV`

Make TV the subject of formula

`TV = 131 - 63`

`TV = 68`

Solving (2):

Given

`MN = 26`

`MP = x + 4`

`PN = 2x + 1`

Required

FInd x

To solve x, we make use of the following formula;

`MN = MP + PN`

Substitute values for MP, MN and NP

`26 =x + 4 + 2x + 1`

Collect Like Terms

`2x + x = 26 - 4 -1`

`3x = 21`

Divide both sides by 3

`x = 7`

Solving (3):

Given

`HM = 4x - 12`

`MJ = 3x + 9`

Required

Find x

Since M is the midpoint;

`HM = MJ`

This gives

`4x - 12 = 3x + 9`

Collect Like Terms

`4x - 3x = 12 + 9`

`x = 21`

Solving (4):

Given

`CE = 6x + 2`

`DE = 2x + 4`

Required

FInd CD

Since D is the midpoint;

`CD= DE`

and

`CE = CD + DE`

Substitute CD for DE

`CE = DE + DE`

`CE = 2DE`

Substitute values for CE and DE

`6x + 2 = 2(2x + 4)`

Open Bracket

`6x + 2 = 4x + 8`

Collect Like Terms

`6x - 4x = 8 - 2`

`2x = 6`

Divide both sides by 2

`x = 3`

Recall that;

`CD= DE`

So;

`CD = 2x + 4`

Substitute 2 for x

`CD = 2 * 2 + 4`

`CD = 4 + 4`

`CD = 8`