Question

[10.02] Solve the proportion 2 times x all over 7 times x minus 6 equals 2 over x.. What is the value of x?

x = -1 and x = -7

x = 1 and x = -7

x = 1 and x = 6

x = -1 and x = 6

Answer 1

\[\frac{ 2x }{ 7x-6 }=\frac{ 2 }{ x }\]
is that it?

Answer 2

yes

Answer 3

so cross multiply so:
\[2(7x-6)=2x*x\]
so:\[2x^2=14x-12\]
rewrite that as:
\[2x^2-14x+12=0\]
what factors of 2*12=24 equal -14
so -12 and -2 multiply to 24 and add up to -14 so write the equation as:\[2x^2-12x-2x+12=0\]
factor by grouping so:
\[2x(x-6)-2(x-6)=0\]
factor:
\[(2x-2)(x-6)=0\]
so:
\[2x-2=0\]
or \[x-6=0\]
so:
\[x=6\]or
x=1

Answer 4

the answer is x=1 and x=6

Answer 5

oh ok i got it now thank you