Solve the Inequality for x -23<1-4x-8

$- 23 < 1 - 4 x - 8$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$1 - 4 x - 8 > - 23$

Step 2

Subtract $8$ from $1$ .

$- 4 x - 7 > - 23$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

Add $7$ to both sides of the inequality.

$- 4 x > - 23 + 7$

Add $- 23$ and $7$ .

$- 4 x > - 16$

Step 4

Divide each term in $- 4 x > - 16$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 16$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 16}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 16}{- 4}$

Divide $x$ by $1$ .

$x < \frac{- 16}{- 4}$

Simplify the right side.

Divide $- 16$ by $- 4$ .

$x < 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 4$

Interval Notation:

$(- \infty, 4)$

Solve the Inequality for x -23<1-4x-8

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