Question:
The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?
Answer:
The value of t is reduced by 6 when the value of r is increased by 4
Step-by-step explanation:
Given
[tex]2t + 3r + 6 = 0[/tex]
Required
What happens when r is increased by 4
[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1
Subtract 2t from both sides
[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]
[tex]3r + 6 = - 2t[/tex] --- Equation 2
When r is increased by 4, equation 1 becomes
[tex]2T + 3(r+4) + 6 = 0[/tex]
Note that the increment of r also affects the value of t; hence, the new value of t is represented by T
Open bracket
[tex]2T + 3r+12 + 6 = 0[/tex]
Rearrange
[tex]2T + 3r+6 +12 = 0[/tex]
Substitutr -2t for 3r + 6 [From equation 2]
[tex]2T -2t +12 = 0[/tex]
Make T the subject of formula
[tex]2T = 2t - 12[/tex]
Divide both sides by 2
[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]
[tex]T = t - 6[/tex]
This means that the value of t is reduced by 6 when the value of r is increased by 4
