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When we say "isolate the variable," we mean positioning our variable on one side of the equation all by itself. This is an essential first step in solving equations because it helps us see exactly what the variable equals. Let's begin by addressing any constants (numbers without variables) that may be mingled with the variable on one side of the equation. In the case of our original exercise, the equation is given as \[ \frac{y}{3} + 2 = 10. \]Our goal is to get \( y \) alone. We do this by removing the number 2 by doing the opposite operation, which is subtraction in this case:- Subtract 2 from both sides.
- This updates the equation to \( \frac{y}{3} = 8 \).
By performing this operation, we've successfully isolated the fraction containing the variable. Once a variable stands alone or within a single fraction, we pave the way to solve for it directly.

After solving an equation and getting a potential value for the variable, it's crucial to confirm this solution is correct. This ensures there were no mathematical miscalculations along the way.To check whether \( y = 24 \) is indeed the solution, substitute this value back into the original equation:- Replace \( y \) with 24 in the equation \( \frac{y}{3} + 2 = 10 \).
- The equation becomes \( \frac{24}{3} + 2 \).
- Simplifying \( \frac{24}{3} \) results in 8.
- Adding 2 to 8 gives 10.Both sides of the equation equal the same number: 10. This tells us that \( y = 24 \) is definitely the right solution. Checking the solution helps prevent any algebraic mistakes and confirms the accuracy of our answer.

Fractions in equations can make things seem trickier than they are. However, with the right approach, they can be tackled easily. To eliminate a fraction means to clear it, so it no longer complicates the equation.In our example problem, we reached a point where the equation was \( \frac{y}{3} = 8 \).To clear the fraction:- Multiply every term in the equation by the denominator, which in this equation is 3.
- The left side simplifies from \( 3 \times \frac{y}{3} \) to just \( y \).
- The right side becomes \( 8 \times 3 = 24 \).Now, the equation reads \( y = 24 \). Doing this operation effectively clears the fraction, leaving the variable neatly on one side of the equation. Sometimes, it can feel like bringing down the extra baggage in an equation, allowing it to solve straightforwardly and precisely.