Question

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?

Answer 1

• The solution for the compound inequality is: $-0.5 < x \leq 2$

• The graph is given at the end of the question.

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The compound inequality is given by:

$-7 < 4x - 5 \leq 3$

Thus, we need:

$4x - 5 > -7$ and $4x - 5 \leq 3$

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

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For the first inequality:

$4x - 5 > -7$

$4x > -2$

$x > -\frac{1}{2}$

$x > -0.5$

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For the second inequality:

$4x - 5 \leq 3$

$4x \leq 8$

$x \leq \frac{8}{4}$

$x \leq 2$

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

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