Question

Umm yesh its another

Answer 1

x=6

EF=34

FG=25

Explanation:

59=8x-14+4x+1

59=12x-13

72=12x

x=6

8(6)-14

48-14

34

4(6)+1

24+1

25

Answer 2

-------------------------------------------------------------------------------------------------------------

Answer:
`\textsf{x = 6; EF = 34; FG = 25}`

-------------------------------------------------------------------------------------------------------------

Given:
`\textsf{EF = 8x - 14, FG = 4x + 1, EG = 59}`

Find:
`\textsf{Determine the value of EF and FG}`

Solution: In order to determine the value of EF and FG, we need to first create an equation using the given information. We know that EF is equal to 8x - 14, FG is equal to 4x + 1, and EG is equal to 59. Therefore, the equation would have the following format: EF + FG = EG

Now that we have the format, we can plug in the expressions and then simplify the equation.

• 
  `\textsf{EF + FG = EG}`
• 
  `\textsf{(8x - 14) + (4x + 1) = 59}`

Now, combine like terms on the left side of the equation.

• 
  `\textsf{(8x + 4x) + (-14 + 1) = 59}`
• 
  `\textsf{(12x) + (-13) = 59}`

After combining like terms, we can solve for x by adding 13 to both sides and then dividing both sides by 12 to isolate the x variable.

• 
  `\textsf{(12x) + (-13 + 13) = 59 + 13}`
• 
  `\textsf{12x = 72}`
• 
  `\textsf{12x/12 = 72/12}`
• 
  `\textsf{x = 6}`

Now that we have the value of x, we can plug it into the EF and FG expressions to determine what the length of the segments are.

• 
  `\textsf{EF = 8(6) - 14}`
• 
  `\textsf{EF = 48 - 14}`
• 
  `\textsf{EF = 34}`

• 
  `\textsf{FG = 4(6) + 1}`
• 
  `\textsf{FG = 24 + 1}`
• 
  `\textsf{FG = 25}`

Therefore, we know that the value of the variable x is equal to 6, the length of EF is 34 and the length of FG is 25.