Solve for x 6-x/3+1>2/3

$6 - \frac{x}{3} + 1 > \frac{2}{3}$

Step 1

Add $6$ and $1$ .

$- \frac{x}{3} + 7 > \frac{2}{3}$

Step 2

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

Subtract $7$ from both sides of the inequality.

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

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{3} > \frac{2}{3} - 7 \cdot \frac{3}{3}$

Combine $- 7$ and $\frac{3}{3}$ .

$- \frac{x}{3} > \frac{2}{3} + \frac{- 7 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- \frac{x}{3} > \frac{2 - 7 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 7$ by $3$ .

$- \frac{x}{3} > \frac{2 - 21}{3}$

Subtract $21$ from $2$ .

$- \frac{x}{3} > \frac{- 19}{3}$

Move the negative in front of the fraction.

$- \frac{x}{3} > - \frac{19}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x > - 19$

Step 4

Divide each term in $- x > - 19$ by $- 1$ and simplify.

Divide each term in $- x > - 19$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 19}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 19}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 19}{- 1}$

Simplify the right side.

Divide $- 19$ by $- 1$ .

$x < 19$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 19$

Interval Notation:

$(- \infty, 19)$

Solve for x 6-x/3+1>2/3

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