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(2x-3)/(5)-(x)/(3) <= 2

2x−35−x3≤2 \frac{2 x-3}{5}-\frac{x}{3} \leq 2

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Full solution

Q. 2x−35−x3≤2 \frac{2 x-3}{5}-\frac{x}{3} \leq 2
  1. Find Common Denominator: Find a common denominator to combine the fractions on the left side of the inequality.\newlineThe common denominator for 55 and 33 is 1515.\newlineMultiply each term by 1515 to eliminate the denominators.\newline$(\(15\) \times (\(2\)x\(-3\)))/\(5\) - (\(15\) \times x)/\(3\) \leq \(15\) \times \(2\)
  2. Multiply and Eliminate Denominators: Simplify each term.\(\newline\)\((3 \times (2x-3)) - (5 \times x) \leq 30\)\(\newline\)\(6x - 9 - 5x \leq 30\)
  3. Simplify Terms: Combine like terms on the left side of the inequality.\(\newline\)\(6x - 5x - 9 \leq 30\)\(\newline\)\(x - 9 \leq 30\)
  4. Combine Like Terms: Isolate the variable \(x\) on one side of the inequality.\(\newline\)Add \(9\) to both sides of the inequality.\(\newline\)\(x - 9 + 9 \leq 30 + 9\)\(\newline\)\(x \leq 39\)
  5. Isolate Variable: Write the final solution as an inequality.\(\newline\)The solution to the inequality is \(x \leq 39\).

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