Question - Clearing and Solving an Equation
Solution:
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 $$ x = 1 $$.
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