Solve -6/5geq5-3x/6

$$- \frac{ 6 }{ 5 } \geq \frac{ 5-3x }{ 6 }$$

Solve for x

$$x\geq \frac{61}{15}$$

Solution Steps

Multiply both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$-\frac{6}{5}\times 6\geq 5-3x$$

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

$$\frac{-6\times 6}{5}\geq 5-3x$$

Multiply -6 and 6 to get -36.

$$\frac{-36}{5}\geq 5-3x$$

Fraction \frac{-36}{5} can be rewritten as -\frac{36}{5} by extracting the negative sign.

$$-\frac{36}{5}\geq 5-3x$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$5-3x\leq -\frac{36}{5}$$

Subtract 5 from both sides.

$$-3x\leq -\frac{36}{5}-5$$

Convert 5 to fraction \frac{25}{5}.

$$-3x\leq -\frac{36}{5}-\frac{25}{5}$$

Since -\frac{36}{5} and \frac{25}{5} have the same denominator, subtract them by subtracting their numerators.

$$-3x\leq \frac{-36-25}{5}$$

Subtract 25 from -36 to get -61.

$$-3x\leq -\frac{61}{5}$$

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

$$x\geq \frac{-\frac{61}{5}}{-3}$$

Express \frac{-\frac{61}{5}}{-3} as a single fraction.

$$x\geq \frac{-61}{5\left(-3\right)}$$

Multiply 5 and -3 to get -15.

$$x\geq \frac{-61}{-15}$$

Fraction \frac{-61}{-15} can be simplified to \frac{61}{15} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{61}{15}$$