Solve the Inequality for x 2(4x+1)<3(2x-3)

$2 (4 x + 1) < 3 (2 x - 3)$

Simplify $2 (4 x + 1)$ .

Start simplifying.

$0 + 0 + 2 (4 x + 1) < 3 (2 x - 3)$

Simplify by adding zeros.

$2 (4 x + 1) < 3 (2 x - 3)$

Apply the distributive property.

$2 (4 x) + 2 \cdot 1 < 3 (2 x - 3)$

Multiply.

Multiply $4$ by $2$ .

$8 x + 2 \cdot 1 < 3 (2 x - 3)$

Multiply $2$ by $1$ .

$8 x + 2 < 3 (2 x - 3)$

Simplify $3 (2 x - 3)$ .

Apply the distributive property.

$8 x + 2 < 3 (2 x) + 3 \cdot - 3$

Multiply.

Multiply $2$ by $3$ .

$8 x + 2 < 6 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$8 x + 2 < 6 x - 9$

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

Subtract $6 x$ from both sides of the inequality.

$8 x + 2 - 6 x < - 9$

Subtract $6 x$ from $8 x$ .

$2 x + 2 < - 9$

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

Subtract $2$ from both sides of the inequality.

$2 x < - 9 - 2$

Subtract $2$ from $- 9$ .

$2 x < - 11$

Divide each term in $2 x < - 11$ by $2$ and simplify.

Divide each term in $2 x < - 11$ by $2$ .

$\frac{2 x}{2} < \frac{- 11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 11}{2}$

Divide $x$ by $1$ .

$x < \frac{- 11}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{11}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{11}{2}$

Interval Notation:

$(- \infty, - \frac{11}{2})$

Solve the Inequality for x 2(4x+1)<3(2x-3)

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