Precalculus Examples

$4 x - 2 < x + 8 < 9 x + 1$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

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Step 1.1

Subtract $8$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$4 x - 2 - 8 < x < 9 x + 1 - 8$

Step 1.2

Subtract $8$ from $- 2$ .

$4 x - 10 < x < 9 x + 1 - 8$

Step 1.3

Subtract $8$ from $1$ .

$4 x - 10 < x < 9 x - 7$

Step 2

Convert the inequality to interval notation.

$(4 x - 10, 9 x - 7)$

Step 3