Solve the Inequality for x -2x>=10x-9(x-1/3)-7

$- 2 x \geq 10 x - 9 (x - \frac{1}{3}) - 7$

Rewrite so $x$ is on the left side of the inequality.

$10 x - 9 (x - \frac{1}{3}) - 7 \leq - 2 x$

Simplify $10 x - 9 (x - \frac{1}{3}) - 7$ .

Simplify each term.

Apply the distributive property.

$10 x - 9 x - 9 (- \frac{1}{3}) - 7 \leq - 2 x$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$10 x - 9 x - 9 (\frac{- 1}{3}) - 7 \leq - 2 x$

Factor $3$ out of $- 9$ .

$10 x - 9 x + 3 (- 3) \frac{- 1}{3} - 7 \leq - 2 x$

Cancel the common factor.

$10 x - 9 x + 3 \cdot - 3 \frac{- 1}{3} - 7 \leq - 2 x$

Rewrite the expression.

$10 x - 9 x - 3 \cdot - 1 - 7 \leq - 2 x$

Multiply $- 3$ by $- 1$ .

$10 x - 9 x + 3 - 7 \leq - 2 x$

Simplify by adding terms.

Subtract $9 x$ from $10 x$ .

$x + 3 - 7 \leq - 2 x$

Subtract $7$ from $3$ .

$x - 4 \leq - 2 x$

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

Add $2 x$ to both sides of the inequality.

$x - 4 + 2 x \leq 0$

Add $x$ and $2 x$ .

$3 x - 4 \leq 0$

Add $4$ to both sides of the inequality.

$3 x \leq 4$

Divide each term in $3 x \leq 4$ by $3$ and simplify.

Divide each term in $3 x \leq 4$ by $3$ .

$\frac{3 x}{3} \leq \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{4}{3}$

Divide $x$ by $1$ .

$x \leq \frac{4}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{4}{3}$

Interval Notation:

$(- \infty, \frac{4}{3}]$