Solve for x 4x+1<8x-3<4x+5

$4 x + 1 < 8 x - 3 < 4 x + 5$

Solve $4 x + 1 < 8 x - 3$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Subtract $8 x$ from both sides of the inequality.

$4 x + 1 - 8 x < - 3$

Subtract $8 x$ from $4 x$ .

$- 4 x + 1 < - 3$

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

Subtract $1$ from both sides of the inequality.

$- 4 x < - 3 - 1$

Subtract $1$ from $- 3$ .

$- 4 x < - 4$

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

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

$\frac{- 4 x}{- 4} > \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{- 4}{- 4}$

Divide $x$ by $1$ .

$x > \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x > 1$

Solve $8 x - 3 < 4 x + 5$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Subtract $4 x$ from both sides of the inequality.

$8 x - 3 - 4 x < 5$

Subtract $4 x$ from $8 x$ .

$4 x - 3 < 5$

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

Add $3$ to both sides of the inequality.

$4 x < 5 + 3$

Add $5$ and $3$ .

$4 x < 8$

Divide each term in $4 x < 8$ by $4$ and simplify.

Divide each term in $4 x < 8$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $4$ .

$x < 2$

Find the intersection of $x > 1$ and $x < 2$ .

$1 < x < 2$

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 2$

Interval Notation:

$(1, 2)$

Solve for x 4x+1<8x-3<4x+5

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