Answer:
The number is -2
Step-by-step explanation:
step 1
Find the reciprocal of 2/3
Remember that when multiply a number by its reciprocal, the result is 1
so
The reciprocal of 2/3 is 3/2
step 2
Let
x-----> the number added to the numerator and denominator
[tex]\frac{23+x}{12-x}=\frac{3}{2}[/tex]
Solve for x
[tex]2(23+x)=3(12-x)\\46+2x=36-3x\\2x+3x=36-46\\5x=-10\\x=-2[/tex]
step 3
verify
[tex]\frac{23+x}{12-x}[/tex]
substitute x=-2
[tex]\frac{23-2}{12+2}[/tex]
[tex]\frac{21}{14}[/tex]
Simplify
[tex]\frac{3}{2}[/tex] ----> is ok
therefore
The number is -2
