Solve the equation 60x = 35.

Step-by-step solution

1. 1

   Divide both sides by the coefficient. The variable is multiplied by $60$, so dividing by $60$ isolates it in one step:

   $x=\frac{35}{60}$

   The answer is a fraction, not an integer — $60$ does not divide $35$ — and leaving it as a fraction keeps it exact.

2. 2

   Reduce the fraction. Factor both parts: $35=5\times7$ and $60=5\times12$, so the greatest common divisor is $5$:

   $x=\frac{35\div5}{60\div5}=\frac{7}{12}$

   Since $7$ is prime and does not divide $12$, this is lowest terms.

3. 3

   Give the decimal form. The denominator $12=2^{2}\times3$ contains a $3$, so the decimal repeats:

   $x=\frac{7}{12}=0.58\overline{3}\approx0.5833$

4. 4

   Verify in the original equation.

   $60\cdot\frac{7}{12}=\frac{60}{12}\cdot7=5\cdot7=35\ \checkmark$

   Cancelling the $12$ into the $60$ first makes the check a single mental step. Confirmed in exact rational arithmetic ✓.

5. 5

   Sanity-check the size. Since $35$ is a bit more than half of $60$, the answer should be a bit more than $\tfrac12$ — and $\tfrac{7}{12}\approx0.583$ is ✓. That quick magnitude check catches a flipped fraction such as $\tfrac{12}{7}$ immediately.