Respuesta :

ANSWER

[tex]\begin{gathered} SN\colon\lbrace x|x\le-\frac{152}{13}\rbrace \\ IN\colon(-\infty,-\frac{152}{13}\rbrack \end{gathered}[/tex]

EXPLANATION

We want to solve the given inequality:

[tex]\frac{3x}{4}-\frac{8x}{2}\ge38[/tex]

First, multiply both sides of the inequality by 4:

[tex]\begin{gathered} (\frac{3x}{4}\cdot4)-(\frac{8x}{2}\cdot4)\ge38\cdot4 \\ \Rightarrow3x-16x\ge152 \end{gathered}[/tex]

Now, simplify the left-hand side of the inequality:

[tex]-13x\ge152[/tex]

Finally, divide both sides of the inequality by -13. When this is done, the sign changes direction:

[tex]\begin{gathered} \frac{-13}{-13}x\le\frac{152}{-13} \\ \Rightarrow x\le-\frac{152}{13} \end{gathered}[/tex]

In set notation, we have:

[tex]\mleft\lbrace x|x\le-\frac{152}{13}\mright\rbrace[/tex]

In interval notation, we have:

[tex](-\infty,-\frac{152}{13}\rbrack[/tex]

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