Solve the inequality 2/3x≤5

1 answer

To solve the inequality \( \frac{2}{3}x \leq 5 \), we can follow these steps:

  1. Multiply both sides by 3 to eliminate the fraction:

\[ 3 \cdot \frac{2}{3}x \leq 3 \cdot 5 \]

This simplifies to:

\[ 2x \leq 15 \]

  1. Divide both sides by 2 to solve for \( x \):

\[ \frac{2x}{2} \leq \frac{15}{2} \]

This simplifies to:

\[ x \leq \frac{15}{2} \]

  1. Convert \(\frac{15}{2}\) into a decimal or mixed number, if necessary:

\[ \frac{15}{2} = 7.5 \]

Thus, the solution to the inequality is:

\[ x \leq 7.5 \]

In interval notation, this can be expressed as:

\[ (-\infty, 7.5] \]

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