Solve the Inequality for x 7(x-3)<2(4x-1)

$7 (x - 3) < 2 (4 x - 1)$

Step 1

Simplify $7 (x - 3)$ .

Start simplifying.

$0 + 0 + 7 (x - 3) < 2 (4 x - 1)$

Simplify by adding zeros.

$7 (x - 3) < 2 (4 x - 1)$

Apply the distributive property.

$7 x + 7 \cdot - 3 < 2 (4 x - 1)$

Multiply $7$ by $- 3$ .

$7 x - 21 < 2 (4 x - 1)$

Step 2

Simplify $2 (4 x - 1)$ .

Apply the distributive property.

$7 x - 21 < 2 (4 x) + 2 \cdot - 1$

Multiply.

Multiply $4$ by $2$ .

$7 x - 21 < 8 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$7 x - 21 < 8 x - 2$

Step 3

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

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

$7 x - 21 - 8 x < - 2$

Subtract $8 x$ from $7 x$ .

$- x - 21 < - 2$

Step 4

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

Add $21$ to both sides of the inequality.

$- x < - 2 + 21$

Add $- 2$ and $21$ .

$- x < 19$

Step 5

Divide each term in $- x < 19$ by $- 1$ and simplify.

Divide each term in $- x < 19$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{19}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{19}{- 1}$

Divide $x$ by $1$ .

$x > \frac{19}{- 1}$

Simplify the right side.

Divide $19$ by $- 1$ .

$x > - 19$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 19$

Interval Notation:

$(- 19, \infty)$

Solve the Inequality for x 7(x-3)<2(4x-1)

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