Solve and graph. |3 – v| < 6 Write the inequality as two inequalities without absolute value. Solve the inequality and write the solution set. Graph the solution on a number line.

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Question:

Solve and graph. |3 – v| < 6 Write the inequality as two inequalities without absolute value. Solve the inequality and write the solution set. Graph the solution on a number line.

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Answer:[tex]-3<v<9[/tex]Step-by-step explanation:The inequality [tex]|3-v| < 6[/tex] is equivalent to the system of two inequalities:[tex]\left\{\begin{array}{l}3-v>-6\\ \\3-v<6\end{array}\right.[/tex]Solve each inequality:1. [tex]3-v>-6:[/tex][tex]3-v>-6\\ \\-v>-6-3\\ \\-v>-9\\ \\v<9[/tex]2. [tex]3-v<6:[/tex][tex]-v<6-3\\ \\-v<3\\ \\v>-3[/tex]The solution set to the initial inequality is[tex]-3<v<9[/tex]The graph of this solution set is attached.

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