1/3+(5x)/6 >-(5x)/6-1/3 — step-by-step solution

Let's solve in

ℝ

\frac{1}{3} + \frac{5 x}{6} > - \frac{5 x}{6} - \frac{1}{3}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{1}{3} + \frac{5 x}{6}

\frac{2 + 5 x}{6}

- \frac{5 x}{6} - \frac{1}{3}

\frac{- 5 x + 2 \cdot (-1)}{6}

\frac{2 + 5 x}{6} > \frac{- 5 x + 2 \cdot (-1)}{6}

ⓘ Multiplications are done before additions and subtractions. A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

2 \cdot (-1)

-2

■The minus sign is factored out, changing the sign of each term:

- 5 x - 2

- (5 x + 2)

\frac{2 + 5 x}{6} > - \frac{5 x + 2}{6}

Let's sum the fractions:

\frac{2 + 5 x}{6} + \frac{5 x + 2}{6} > 0

ⓘ Like terms are grouped by adding their coefficients:

\frac{2 + 5 x}{6} + \frac{5 x + 2}{6}

\frac{2 + 5 x}{3}

\frac{2 + 5 x}{3} > 0

⇥The expression

2 + 5 x

is zero at:

⇥

x = - \frac{2}{5}

⇥Its coefficient of

x

5

, being positive, it is negative before and positive after

- \frac{2}{5}

▶Solution found:

x > - \frac{2}{5}

The numeric value of:

x > - \frac{2}{5}

equals:

▷

x > -0.4