# Chapter 6 - Algebra: Equations and Inequalities - 6.4 Linear Inequalities in One Variable - Exercise Set 6.4 - Page 384: 70

$x\ge \frac{7+48y}{6}$.

#### Work Step by Step

Given is an inequality $Ax+By\le C;A<0$, where $A,B,C$ are constants. An equivalent inequality can be found by substituting any values for $A,B,C$, which also fulfills the condition $A<0$. Use the property of inequality, which says that an inequality changes the sign if divided by a negative quantity. An equivalent inequality can be written as follows: $-6x+48y\le -7$ This inequality is restructured with $x$ isolated on left side as: \begin{align} & x\ge \frac{-7-48y}{-6} \\ & x\ge \frac{7+48y}{6} \\ \end{align} The equivalent inequality is given as $x\ge \frac{7+48y}{6}$.

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