Sure, let's solve the expression step-by-step.
Given the expression:
[tex]\[ 5 \left( \frac{x}{y} \right) - x \][/tex]
with [tex]\( x = 6 \)[/tex] and [tex]\( y = \frac{2}{3} \)[/tex].
### Step 1: Substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
We have:
[tex]\[ x = 6 \][/tex]
[tex]\[ y = \frac{2}{3} \][/tex]
### Step 2: Simplify [tex]\( \frac{x}{y} \)[/tex]
Calculate [tex]\( \frac{x}{y} \)[/tex]:
[tex]\[ \frac{x}{y} = \frac{6}{\frac{2}{3}} \][/tex]
To divide by a fraction, we multiply by its reciprocal:
[tex]\[ \frac{6}{\frac{2}{3}} = 6 \times \frac{3}{2} = \frac{18}{2} = 9 \][/tex]
So:
[tex]\[ \frac{x}{y} = 9 \][/tex]
### Step 3: Multiply the result by 5
We now multiply the result by 5:
[tex]\[ 5 \left( \frac{x}{y} \right) = 5 \times 9 = 45 \][/tex]
### Step 4: Subtract [tex]\( x \)[/tex] from the result
Finally, subtract [tex]\( x \)[/tex] from the result:
[tex]\[ 5 \left( \frac{x}{y} \right) - x = 45 - 6 = 39 \][/tex]
### Conclusion
The value of the expression [tex]\( 5\left(\frac{x}{y}\right) - x \)[/tex], when [tex]\( x = 6 \)[/tex] and [tex]\( y = \frac{2}{3} \)[/tex], is [tex]\( 39 \)[/tex].
