Solve the System of @WORD -2<4x-10<6

$- 2 < 4 x - 10 < 6$

Step 1

Solve $- 2 < 4 x - 10$ for $x$ .

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

$4 x - 10 > - 2$

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

Add $10$ to both sides of the inequality.

$4 x > - 2 + 10$

Add $- 2$ and $10$ .

$4 x > 8$

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 $4$ .

$x > 2$

Step 2

Solve $4 x - 10 < 6$ for $x$ .

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

Add $10$ to both sides of the inequality.

$4 x < 6 + 10$

Add $6$ and $10$ .

$4 x < 16$

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

Divide each term in $4 x < 16$ by $4$ .

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

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 3

Find the intersection of $x > 2$ and $x < 4$ .

$2 < x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$2 < x < 4$

Interval Notation:

$(2, 4)$

Step 5

Solve the System of @WORD -2<4x-10<6

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