Solve y-1/2-2leq3y-2

$$y - \frac { 1 } { 2 } - 2 \leq 3 y - 2$$

Solve for y

$$y\geq -\frac{1}{4}$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$y-\frac{1}{2}-\frac{4}{2}\leq 3y-2$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$y+\frac{-1-4}{2}\leq 3y-2$$

Subtract 4 from -1 to get -5.

$$y-\frac{5}{2}\leq 3y-2$$

Subtract 3y from both sides.

$$y-\frac{5}{2}-3y\leq -2$$

Combine y and -3y to get -2y.

$$-2y-\frac{5}{2}\leq -2$$

Add \frac{5}{2} to both sides.

$$-2y\leq -2+\frac{5}{2}$$

Convert -2 to fraction -\frac{4}{2}.

$$-2y\leq -\frac{4}{2}+\frac{5}{2}$$

Since -\frac{4}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$-2y\leq \frac{-4+5}{2}$$

Add -4 and 5 to get 1.

$$-2y\leq \frac{1}{2}$$

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

$$y\geq \frac{\frac{1}{2}}{-2}$$

Express \frac{\frac{1}{2}}{-2} as a single fraction.

$$y\geq \frac{1}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$y\geq \frac{1}{-4}$$

Fraction \frac{1}{-4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$y\geq -\frac{1}{4}$$