Solve 5x+2>3x-3-5/2

$$5 x + 2 > 3 x - 3 - \frac { 5 } { 2 }$$

Solve for x

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

Solution Steps

Convert -3 to fraction -\frac{6}{2}.

$$5x+2>3x-\frac{6}{2}-\frac{5}{2}$$

Since -\frac{6}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$5x+2>3x+\frac{-6-5}{2}$$

Subtract 5 from -6 to get -11.

$$5x+2>3x-\frac{11}{2}$$

Subtract 3x from both sides.

$$5x+2-3x>-\frac{11}{2}$$

Combine 5x and -3x to get 2x.

$$2x+2>-\frac{11}{2}$$

Subtract 2 from both sides.

$$2x>-\frac{11}{2}-2$$

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

$$2x>-\frac{11}{2}-\frac{4}{2}$$

Since -\frac{11}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$2x>\frac{-11-4}{2}$$

Subtract 4 from -11 to get -15.

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

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

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

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

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

Multiply 2 and 2 to get 4.

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

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

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