Solve 275-3x/4>-3

$$27 \frac { 5 - 3 x } { 4 } > - 3$$

Solve for x

$$x<\frac{49}{27}$$

Solution Steps

Divide both sides by 27. Since 27 is positive, the inequality direction remains the same.

$$\frac{5-3x}{4}>\frac{-3}{27}$$

Reduce the fraction \frac{-3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{5-3x}{4}>-\frac{1}{9}$$

Multiply both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$5-3x>-\frac{1}{9}\times 4$$

Express -\frac{1}{9}\times 4 as a single fraction.

$$5-3x>\frac{-4}{9}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$5-3x>-\frac{4}{9}$$

Subtract 5 from both sides.

$$-3x>-\frac{4}{9}-5$$

Convert 5 to fraction \frac{45}{9}.

$$-3x>-\frac{4}{9}-\frac{45}{9}$$

Since -\frac{4}{9} and \frac{45}{9} have the same denominator, subtract them by subtracting their numerators.

$$-3x>\frac{-4-45}{9}$$

Subtract 45 from -4 to get -49.

$$-3x>-\frac{49}{9}$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-\frac{49}{9}}{-3}$$

Express \frac{-\frac{49}{9}}{-3} as a single fraction.

$$x<\frac{-49}{9\left(-3\right)}$$

Multiply 9 and -3 to get -27.

$$x<\frac{-49}{-27}$$

Fraction \frac{-49}{-27} can be simplified to \frac{49}{27} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{49}{27}$$