Solve for x 6x>4(x-7)+17

$6 x > 4 (x - 7) + 17$

Step 1

Simplify $4 (x - 7) + 17$ .

Simplify each term.

Apply the distributive property.

$6 x > 4 x + 4 \cdot - 7 + 17$

Multiply $4$ by $- 7$ .

$6 x > 4 x - 28 + 17$

Add $- 28$ and $17$ .

$6 x > 4 x - 11$

Step 2

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

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

$6 x - 4 x > - 11$

Subtract $4 x$ from $6 x$ .

$2 x > - 11$

Step 3

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.

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

Step 4

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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