Respuesta :
Answer:
PART A:
[tex]24(mx + n) = 3x + 17[/tex]
when m is 14 and n is 13:
[tex]24 \{(14)x + 13) = 3x + 17 \\ 24(14x + 13) = 3x + 17 \\ 336x + 312 = 3x + 17[/tex]
collect like terms:
[tex]336x - 3x = 17 - 312 \\ 333x = - 295 \\ x = - 0.886 \\ \\ { \boxed{ \boxed{ \sf{it \: has \: one \: solution}}}}[/tex]
PART B:
[tex]if \: m \: is \: 18 \\ 24(18x + n) = 3x + 17 \\ [/tex]
remember x is -0.886
[tex]24 \{(18 \times - 0.886) + n \} = (3 \times - 0.886) + 17 \\ - 382.752 + 24n = - 26.58 \\ 24n = 356.172 \\ { \boxed{ \boxed{ \sf{n \: is \: 14.8}}}}[/tex]
- The given equation has one solution at x = 0.886 .
- Equation have infinitely many solution when n = -15.41 .
Given equation;
24( mx + n ) = 3x + 17
where m and n are real numbers.
- Part 1 ; If m = 14 and n = 13;
Putting the value of m and n in the given equation.
= 24( 14.x + 13 ) = 3x + 17
= 336x + 312 = 3x + 17
= 336x - 3x = 17- 312
= 333x = -295
= x = [tex]\frac{-295}{333}[/tex]
= x = 0.886
Thus x = 0.886 we can say that the equation having one solution .
A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.
- part 2 ; if m = 18 then find n .
put m = 18 in the given equation
= 24(18.(0.886) + n ) = 3(0.886) + 17
= 24(15.94) + 24n = 2.658 + 17
= 382.56 + 24n = 19.658
= 24n = 19.658 - 382.56
= n = [tex]\frac{-362.97}{24}[/tex]
= n = -15.41
The equation have infinitely many solution when n = -15.41.
For more details about the types of solution click the click given below.
https://brainly.com/question/21400387
