Solve the Inequality for x 1-4/7>6x+2/7-5x

$1 - \frac{4}{7} > 6 x + \frac{2}{7} - 5 x$

Step 1

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

$6 x + \frac{2}{7} - 5 x < 1 - \frac{4}{7}$

Step 2

Subtract $5 x$ from $6 x$ .

$x + \frac{2}{7} < 1 - \frac{4}{7}$

Step 3

Simplify $1 - \frac{4}{7}$ .

Write $1$ as a fraction with a common denominator.

$x + \frac{2}{7} < \frac{7}{7} - \frac{4}{7}$

Combine the numerators over the common denominator.

$x + \frac{2}{7} < \frac{7 - 4}{7}$

Subtract $4$ from $7$ .

$x + \frac{2}{7} < \frac{3}{7}$

Step 4

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

Subtract $\frac{2}{7}$ from both sides of the inequality.

$x < \frac{3}{7} - \frac{2}{7}$

Combine the numerators over the common denominator.

$x < \frac{3 - 2}{7}$

Subtract $2$ from $3$ .

$x < \frac{1}{7}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{1}{7}$

Interval Notation:

$(- \infty, \frac{1}{7})$