Solve the Inequality for x 3(2-3x)>5(1-4x)

$3 (2 - 3 x) > 5 (1 - 4 x)$

Step 1

Simplify $3 (2 - 3 x)$ .

Start simplifying.

$0 + 0 + 3 (2 - 3 x) > 5 (1 - 4 x)$

Simplify by adding zeros.

$3 (2 - 3 x) > 5 (1 - 4 x)$

Apply the distributive property.

$3 \cdot 2 + 3 (- 3 x) > 5 (1 - 4 x)$

Multiply.

Multiply $3$ by $2$ .

$6 + 3 (- 3 x) > 5 (1 - 4 x)$

Multiply $- 3$ by $3$ .

$6 - 9 x > 5 (1 - 4 x)$

Step 2

Simplify $5 (1 - 4 x)$ .

Apply the distributive property.

$6 - 9 x > 5 \cdot 1 + 5 (- 4 x)$

Multiply.

Multiply $5$ by $1$ .

$6 - 9 x > 5 + 5 (- 4 x)$

Multiply $- 4$ by $5$ .

$6 - 9 x > 5 - 20 x$

Step 3

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

Add $20 x$ to both sides of the inequality.

$6 - 9 x + 20 x > 5$

Add $- 9 x$ and $20 x$ .

$6 + 11 x > 5$

Step 4

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

Subtract $6$ from both sides of the inequality.

$11 x > 5 - 6$

Subtract $6$ from $5$ .

$11 x > - 1$

Step 5

Divide each term in $11 x > - 1$ by $11$ and simplify.

Divide each term in $11 x > - 1$ by $11$ .

$\frac{11 x}{11} > \frac{- 1}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} > \frac{- 1}{11}$

Divide $x$ by $1$ .

$x > \frac{- 1}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{1}{11}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{11}$

Interval Notation:

$(- \frac{1}{11}, \infty)$

Solve the Inequality for x 3(2-3x)>5(1-4x)

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