Solve 3/2left(1/2-xright)>x/2-3

$$\frac{ 3 }{ 2 } \left( \frac{ 1 }{ 2 } -x \right) > \frac{ x }{ 2 } -3$$

Solve for x

$$x<\frac{15}{8}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$3\left(\frac{1}{2}-x\right)>x-6$$

Use the distributive property to multiply 3 by \frac{1}{2}-x.

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

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

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

Subtract x from both sides.

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

Combine -3x and -x to get -4x.

$$\frac{3}{2}-4x>-6$$

Subtract \frac{3}{2} from both sides.

$$-4x>-6-\frac{3}{2}$$

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

$$-4x>-\frac{12}{2}-\frac{3}{2}$$

Since -\frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-4x>\frac{-12-3}{2}$$

Subtract 3 from -12 to get -15.

$$-4x>-\frac{15}{2}$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-\frac{15}{2}}{-4}$$

Express \frac{-\frac{15}{2}}{-4} as a single fraction.

$$x<\frac{-15}{2\left(-4\right)}$$

Multiply 2 and -4 to get -8.

$$x<\frac{-15}{-8}$$

Fraction \frac{-15}{-8} can be simplified to \frac{15}{8} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{15}{8}$$