Question

Determine a value for b tht makes 1.7 the solution of the equation 2(5–bx)=15.1–7x. then determine a value of b that results in no solution.

Answer 1

1)
Substitute 1.7 for x in the equation.


`2(5-bx)=15.1-7x \\ 2(5-b * 1.7)=15.1 - 7 * 1.7 \\ 2(5-1.7b)=15.1-11.9 \\ 10-3.4b=3.2 \\ -3.4b=3.2-10 \\ -3.4b=-6.8 \\ b=(-6.8)/(-3.4) \\ b=2`

b=2 makes 1.7 the solution of the equation.

2)
First solve the equation for x.


`2(5-bx)=15.1-7x \\ 10-2bx=15.1-7x \\ -2bx+7x=15.1-10 \\ (-2b+7)x=5.1 \\ x=(5.1)/(-2b+7)`

There will be no possible solution if the denominator is equal to 0.


`-2b+7=0 \\ -2b=-7 \\ b=(-7)/(-2) \\ b=3.5`

b=3.5 results in no solution.