Solve the System of @WORD 1<3x-2<4

$1 < 3 x - 2 < 4$

Step 1

Solve $1 < 3 x - 2$ for $x$ .

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

$3 x - 2 > 1$

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

Add $2$ to both sides of the inequality.

$3 x > 1 + 2$

Add $1$ and $2$ .

$3 x > 3$

Divide each term in $3 x > 3$ by $3$ and simplify.

Divide each term in $3 x > 3$ by $3$ .

$\frac{3 x}{3} > \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{3}{3}$

Divide $x$ by $1$ .

$x > \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$x > 1$

Step 2

Solve $3 x - 2 < 4$ for $x$ .

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

Add $2$ to both sides of the inequality.

$3 x < 4 + 2$

Add $4$ and $2$ .

$3 x < 6$

Divide each term in $3 x < 6$ by $3$ and simplify.

Divide each term in $3 x < 6$ by $3$ .

$\frac{3 x}{3} < \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{6}{3}$

Divide $x$ by $1$ .

$x < \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x < 2$

Step 3

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

$1 < x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 2$

Interval Notation:

$(1, 2)$

Step 5

Solve the System of @WORD 1<3x-2<4

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