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Sebastian solves each inequality in the compound inequality -7 < 4x -5 less than or equal to 3. He gets the solution x greater than - 1/2 for -7 < 4x -5 and the solution x less than or equal to 2 for 4x -5 less than or equal to 3. Which graph represents the solution set of the compound inequality?

Respuesta :

  • The solution for the compound inequality is: [tex]-0.5 < x \leq 2[/tex]
  • The graph is given at the end of the question.

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The compound inequality is given by:

[tex]-7 < 4x - 5 \leq 3[/tex]

Thus, we need:

[tex]4x - 5 > -7[/tex] and [tex]4x - 5 \leq 3[/tex]

That is, values of x that respect both these conditions.

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For the first inequality:

[tex]4x - 5 > -7[/tex]

[tex]4x > -2[/tex]

[tex]x > -\frac{1}{2}[/tex]

[tex]x > -0.5[/tex]

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For the second inequality:

[tex]4x - 5 \leq 3[/tex]

[tex]4x \leq 8[/tex]

[tex]x \leq \frac{8}{4}[/tex]

[tex]x \leq 2[/tex]

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  • Considering that both conditions are needed, the solution is: [tex]-0.5 < x \leq 2[/tex]
  • The graph on the number line is given next.

A similar problem is given at https://brainly.com/question/24009950

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