Example Question - clearing an equation

Clearing and Solving an Equation

The image depicts an equation that is written somewhat unclearly and upside down. Let me first interpret the equation correctly and then solve it for you. The equation appears to be: \[ \frac{x}{5} + \frac{x}{2} = \frac{7}{10} \] Let's solve it step by step: 1. Find a common denominator for the fractions on the left side of the equation. The least common denominator (LCD) for 5 and 2 is 10. 2. Convert each fraction to an equivalent fraction with the LCD as the denominator: \[ \frac{x}{5} = \frac{2x}{10} \] \[ \frac{x}{2} = \frac{5x}{10} \] The equation now looks like this: \[ \frac{2x}{10} + \frac{5x}{10} = \frac{7}{10} \] 3. Combine the fractions on the left side by adding their numerators: \[ \frac{2x + 5x}{10} = \frac{7}{10} \] Which simplifies to: \[ \frac{7x}{10} = \frac{7}{10} \] 4. Since the denominators are the same, we can set the numerators equal to each other: \[ 7x = 7 \] 5. Divide both sides by 7 to solve for x: \[ \frac{7x}{7} = \frac{7}{7} \] \[ x = 1 \] So the solution to the equation is \( x = 1 \).