Solve for x -9<4x+3<27 enter your answer as one inequality in the box

Inequality in mathematics is a relation that helps us to compare two or more mathematical expressions. The expressions can be related to each other using the following operators > (greater then), < (less then), ≥ (greater then or equal to), ≤ (less then or equal to). Yes, the inequality [tex]a < b < c[/tex] signifies (or means) that [tex]a < b[/tex] and [tex]b < c[/tex].

[tex]a < b < c \; \;\;means\; \;\;a < b\; \;and\; \;b < c[/tex]

Using the above rule, we can also solve the inequality given to us :[tex]x-9 < 4x +3 < 27[/tex] by separating it into two different inequalities as follows-

[tex]x-9 < 4x+3[/tex] (Inequality 1)

and

[tex]4x + 3 < 27[/tex] (Inequality 2)

Solving the Inequality - 1 :

[tex]x-9 < 4x+3[/tex]

Subtracting [tex]x[/tex] on both sides, we get -

[tex]x-9-x < 4x-x+3\\\\-9 < 3x+3[/tex]

Adding [tex]-3[/tex] on both sides, we get -

[tex]-3-9 < 3x+3-3\\-12 < 3x[/tex]

Dividing both sides by [tex]3[/tex]. we get -

[tex]\frac{-12}{3} < \frac{3x}{3}[/tex]

[tex]x > -4[/tex]

Solving the Inequality - 2 :

[tex]4x+3 < 27[/tex]

Subtracting [tex]3[/tex] from both sides, we get -

[tex]4x+3-3 < 27-3\\4x < 24[/tex]

Dividing both sides by [tex]4\\[/tex]. we get -

[tex]\frac{4x}{4} < \frac{24}{4}[/tex]

[tex]x < 6[/tex]

Now, on solving the above two inequalities, we got the following result -

[tex]x > -4[/tex] and [tex]x < 6[/tex]. Combining both to one inequality, we get -

[tex]-4 < x < 6[/tex]

Hence, the solution for the inequality - [tex]x-9 < 4x+3 < 27[/tex] can be written in one-inequality as -

[tex]-4 < x < 6[/tex]

To solve more questions on finding the solution of linear inequalities, visit the following link -

https://brainly.com/question/17675534

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