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

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

Step 1

Simplify $4 (x - 2)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

$7 x + 1 < 4 x + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$7 x + 1 < 4 x - 8$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$7 x + 1 - 4 x < - 8$

Subtract $4 x$ from $7 x$ .

$3 x + 1 < - 8$

Step 3

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

Subtract $1$ from both sides of the inequality.

$3 x < - 8 - 1$

Subtract $1$ from $- 8$ .

$3 x < - 9$

Step 4

Divide each term in $3 x < - 9$ by $3$ and simplify.

Divide each term in $3 x < - 9$ by $3$ .

$\frac{3 x}{3} < \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 9}{3}$

Divide $x$ by $1$ .

$x < \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x < - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 3$

Interval Notation:

$(- \infty, - 3)$