# Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set: 86

$x\ge2$

#### Work Step by Step

Remember that when we divide or multiply an inequality by a negative, we have to flip the sign of the inequality. Using the properties of inequality, the solution to the given inequality, $\dfrac{2}{3}-\dfrac{x}{5}\le\dfrac{4}{15} ,$ is \begin{array}{l}\require{cancel} 15\left( \dfrac{2}{3}-\dfrac{x}{5} \right)\le\left(\dfrac{4}{15} \right)15 \\\\ 5(2)-3(x)\le4(1) \\\\ 10-3x\le4 \\\\ -3x\le4-10 \\\\ -3x\le-6 \\\\ x\ge\dfrac{-6}{-3} \\\\ x\ge2 .\end{array}

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