Solve -1/2x-2<9/2x+5/6

$$- \frac { 1 } { 2 } x - 2 < \frac { 9 } { 2 } x + \frac { 5 } { 6 }$$

Solve for x

$$x>-\frac{17}{30}$$

Solution Steps

Subtract \frac{9}{2}x from both sides.

$$-\frac{1}{2}x-2-\frac{9}{2}x<\frac{5}{6}$$

Combine -\frac{1}{2}x and -\frac{9}{2}x to get -5x.

$$-5x-2<\frac{5}{6}$$

Add 2 to both sides.

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

Convert 2 to fraction \frac{12}{6}.

$$-5x<\frac{5}{6}+\frac{12}{6}$$

Since \frac{5}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$-5x<\frac{5+12}{6}$$

Add 5 and 12 to get 17.

$$-5x<\frac{17}{6}$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{\frac{17}{6}}{-5}$$

Express \frac{\frac{17}{6}}{-5} as a single fraction.

$$x>\frac{17}{6\left(-5\right)}$$

Multiply 6 and -5 to get -30.

$$x>\frac{17}{-30}$$

Fraction \frac{17}{-30} can be rewritten as -\frac{17}{30} by extracting the negative sign.

$$x>-\frac{17}{30}$$