Question

1. complete the steps to solve the equation.

\\(\frac{1}{5}t + 2 - square = 17 - square\\)
\\(\frac{1}{5}t = square\\)
\\(square \cdot \frac{1}{5}t = square\\)
\\(t = square\\)

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( t \), we subtract 2 from both sides of the equation \(\frac{1}{5}t + 2 - \boldsymbol{2}= 17 - \boldsymbol{2}\)

Step2: Simplify both sides

Simplifying the left side: \(\frac{1}{5}t + (2 - 2)=\frac{1}{5}t\)
Simplifying the right side: \(17 - 2 = 15\), so \(\frac{1}{5}t=\boldsymbol{15}\)

Step3: Multiply by reciprocal of \(\frac{1}{5}\)

The reciprocal of \(\frac{1}{5}\) is 5. So we multiply both sides by 5: \(\boldsymbol{5}\cdot\frac{1}{5}t = 5\cdot\boldsymbol{15}\)

Step4: Simplify to solve for \(t\)

Simplifying the left side: \(5\cdot\frac{1}{5}t=t\)
Simplifying the right side: \(5\cdot15 = 75\), so \(t=\boldsymbol{75}\)

Answer:

First two boxes: \(2\), \(2\); Third box: \(15\); Fourth box: \(5\); Fifth box: \(75\); Sixth box: \(75\) (Filling order: first box in the first row, second box in the first row, box after \(\frac{1}{5}t=\), first box in the multiplication row, second box in the multiplication row, box after \(t=\))