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Graph the solution set of the inequality and write the solution using interval notation. Please give me a step by step explanation.

Graph the solution set of the inequality and write the solution using interval notation-example-1

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We have the inequality:

-4 < (3x - 2)/5 ≤ 6

We multiply all the sides by 5:

-4*5 < 5*(3x - 2)/5 ≤ 6*5

-20 < 3x - 2 ≤ 30

Now, we add 2 to all the sides of the inequality:

-20 + 2 < 3x - 2 + 2 ≤ 30 + 2

-18 < 3x ≤ 32

Finally, we divide by 3:

-18/3 < 3x/3 ≤ 32/3

-6 < x < 32/3

Now, using interval notation:

x = (-6, 32/3]

This means that x takes all the values greater than -6 and less or equal to 32/3. Graphically, this is:

Graph the solution set of the inequality and write the solution using interval notation-example-1
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