### Instruction: Solve for $x$: $x = \dfrac{35}{6-\frac{2}{5}}$.### Response: I need to isolate $x$ on one side of the equation, so I want to get rid of the fraction on the right side.
To do that, I can multiply both sides by the denominator of the fraction, which is $6-\frac{2}{5}$.
That will cancel out the fraction on the right side, and leave me with $x(6-\frac{2}{5}) = 35$ on the left side.
Now I need to simplify the expression on the left side by distributing $x$ over the parentheses.
That will give me $6x - \frac{2}{5}x = 35$.
To combine the terms with $x$, I need to have a common denominator for the coefficients.
So I can multiply the first term by $\frac{5}{5}$, which is equivalent to 1, and get $\frac{30}{5}x - \frac{2}{5}x = 35$.
Now I can subtract the coefficients and get $\frac{28}{5}x = 35$.
To solve for $x$, I need to divide both sides by $\frac{28}{5}$, which is the same as multiplying by the reciprocal, $\frac{5}{28}$.
That will give me $x = 35 \times \frac{5}{28}$.
To simplify the fraction, I can divide the numerator and denominator by 7, which is a common factor.
That will give me $x = 5 \times \frac{5}{4}$.
To write the fraction as a mixed number, I can divide 5 by 4 and get 1 with a remainder of 1.