Solve the Inequality for x 0.2(x+20)-3>-7-6.2x

$0.2 (x + 20) - 3 > - 7 - 6.2 x$

Step 1

Simplify $0.2 (x + 20) - 3$ .

Simplify each term.

Apply the distributive property.

$0.2 x + 0.2 \cdot 20 - 3 > - 7 - 6.2 x$

Multiply $0.2$ by $20$ .

$0.2 x + 4 - 3 > - 7 - 6.2 x$

Subtract $3$ from $4$ .

$0.2 x + 1 > - 7 - 6.2 x$

Step 2

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

Add $6.2 x$ to both sides of the inequality.

$0.2 x + 1 + 6.2 x > - 7$

Add $0.2 x$ and $6.2 x$ .

$6.4 x + 1 > - 7$

Step 3

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

Subtract $1$ from both sides of the inequality.

$6.4 x > - 7 - 1$

Subtract $1$ from $- 7$ .

$6.4 x > - 8$

Step 4

Divide each term in $6.4 x > - 8$ by $6.4$ and simplify.

Divide each term in $6.4 x > - 8$ by $6.4$ .

$\frac{6.4 x}{6.4} > \frac{- 8}{6.4}$

Simplify the left side.

Cancel the common factor of $6.4$ .

Cancel the common factor.

$\frac{6.4 x}{6.4} > \frac{- 8}{6.4}$

Divide $x$ by $1$ .

$x > \frac{- 8}{6.4}$

Simplify the right side.

Divide $- 8$ by $6.4$ .

$x > - 1.25$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 1.25$

Interval Notation:

$(- 1.25, \infty)$