Solve 4x+2/5>6x-1

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

Solve for x

$$x<\frac{7}{10}$$

Solution Steps

Subtract 6x from both sides.

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

Combine 4x and -6x to get -2x.

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

Subtract \frac{2}{5} from both sides.

$$-2x>-1-\frac{2}{5}$$

Convert -1 to fraction -\frac{5}{5}.

$$-2x>-\frac{5}{5}-\frac{2}{5}$$

Since -\frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$-2x>\frac{-5-2}{5}$$

Subtract 2 from -5 to get -7.

$$-2x>-\frac{7}{5}$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x<\frac{-\frac{7}{5}}{-2}$$

Express \frac{-\frac{7}{5}}{-2} as a single fraction.

$$x<\frac{-7}{5\left(-2\right)}$$

Multiply 5 and -2 to get -10.

$$x<\frac{-7}{-10}$$

Fraction \frac{-7}{-10} can be simplified to \frac{7}{10} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{7}{10}$$