Questions: Solve for x : 1/5 x + 1/3 = 1

Transcript text: Solve for $x$ : \[ \frac{1}{5} x+\frac{1}{3}=1 \]

Solution

Solution Steps

To solve the equation $\frac{1}{5} x + \frac{1}{3} = 1$, we need to isolate $x$. First, subtract $\frac{1}{3}$ from both sides to get $\frac{1}{5} x = 1 - \frac{1}{3}$. Then, find a common denominator to simplify the right side of the equation. Finally, multiply both sides by 5 to solve for $x$.

Step 1: Set Up the Equation

We start with the equation: \[ \frac{1}{5} x + \frac{1}{3} = 1 \]

Step 2: Isolate $x$

To isolate $x$, we first subtract $\frac{1}{3}$ from both sides: \[ \frac{1}{5} x = 1 - \frac{1}{3} \] Calculating the right side, we find: \[ 1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3} \] Thus, we have: \[ \frac{1}{5} x = \frac{2}{3} \]

Step 3: Solve for $x$

Next, we multiply both sides by 5 to solve for $x$: \[ x = 5 \cdot \frac{2}{3} = \frac{10}{3} \]