Example Question - fraction expression
Here are examples of questions we've helped users solve.
Solving a Fraction Expression
The image is a bit blurry, but it looks like the expression is a fraction where the numerator is \( \frac{1}{7x^2y^3} \) and the denominator is \( \frac{1}{3x^3y} \). To solve this expression, you can simply invert the denominator and multiply it with the numerator: \( (\frac{1}{7x^2y^3}) \times (\frac{3x^3y}{1}) \) When you multiply fractions, you multiply the numerators together and the denominators together: \( \frac{1 \times 3x^3y}{7x^2y^3 \times 1} \) \( \frac{3x^3y}{7x^2y^3} \) Now simplify by canceling out the common terms: The \( x^2 \) in the denominator cancels out with two of the \( x \)s in the numerator, leaving you with one \( x \) in the numerator. Similarly, the \( y \) in the numerator and one \( y \) in the denominator will cancel out, leaving you with \( y^2 \) in the denominator. So, you're left with: \( \frac{3x}{7y^2} \) This is the simplified form of the given expression.
Solving Absolute Value Inequality
To solve the inequality \( 3 \left| \frac{x+3}{2} \right| \leq 9 \), we can proceed as follows: 1. Divide both sides of the inequality by 3 to isolate the absolute value expression: \[ \left| \frac{x+3}{2} \right| \leq \frac{9}{3} \] \[ \left| \frac{x+3}{2} \right| \leq 3 \] 2. The absolute value inequality \( |A| \leq B \) where \( B \) is non-negative (B ≥ 0) can be split into two inequalities: \[ -B \leq A \leq B \] Applying this concept, we get: \[ -3 \leq \frac{x+3}{2} \leq 3 \] 3. Multiply all parts of the compound inequality by 2 to get rid of the fraction: \[ -6 \leq x+3 \leq 6 \] 4. Now subtract 3 from all parts of the compound inequality to solve for \( x \): \[ -6 - 3 \leq x+3 - 3 \leq 6 - 3 \] \[ -9 \leq x \leq 3 \] So the solution set for the inequality is \( x \in [-9, 3] \).
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