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Solve the following inequality: $\newline$ 5x < -2(-7x-\frac{1}{2})-6

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Does (x, y) satisfy the inequality?

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Q. Solve the following inequality:

\newline

5x < -2(-7x-\frac{1}{2})-6

Distribute and Simplify: Distribute the $-2$ across the parentheses. $\newline$ $-2 \times -7x = 14x$ $\newline$ $-2 \times -\left(\frac{1}{2}\right) = 1$ $\newline$ So the inequality becomes: $\newline$ 5x < 14x + 1 - 6
Combine Like Terms: Combine like terms on the right side of the inequality. $\newline$ $14x + 1 - 6$ simplifies to $14x - 5$ . $\newline$ Now the inequality is: $\newline$ 5x < 14x - 5
Get $x$ Terms Together: Subtract $14x$ from both sides to get all the $x$ terms on one side. $\newline$ 5x - 14x < -5 $\newline$ This simplifies to: $\newline$ -9x < -5
Divide and Solve: Divide both sides by $-9$ to solve for $x$ . $\newline$ Remember that dividing by a negative number reverses the inequality sign. $\newline$ \frac{-9x}{-9} > \frac{-5}{-9} $\newline$ This simplifies to: $\newline$ x > \frac{5}{9}

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