Solve 12/503-xgeq3x+5

$$\frac { 12 } { 50 } 3 - x \geq 3 x + 5$$

Solve for x

$$x\leq -\frac{107}{100}$$

Solution Steps

Reduce the fraction \frac{12}{50} to lowest terms by extracting and canceling out 2.

$$\frac{6}{25}\times 3-x\geq 3x+5$$

Express \frac{6}{25}\times 3 as a single fraction.

$$\frac{6\times 3}{25}-x\geq 3x+5$$

Multiply 6 and 3 to get 18.

$$\frac{18}{25}-x\geq 3x+5$$

Subtract 3x from both sides.

$$\frac{18}{25}-x-3x\geq 5$$

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

$$\frac{18}{25}-4x\geq 5$$

Subtract \frac{18}{25} from both sides.

$$-4x\geq 5-\frac{18}{25}$$

Convert 5 to fraction \frac{125}{25}.

$$-4x\geq \frac{125}{25}-\frac{18}{25}$$

Since \frac{125}{25} and \frac{18}{25} have the same denominator, subtract them by subtracting their numerators.

$$-4x\geq \frac{125-18}{25}$$

Subtract 18 from 125 to get 107.

$$-4x\geq \frac{107}{25}$$

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

$$x\leq \frac{\frac{107}{25}}{-4}$$

Express \frac{\frac{107}{25}}{-4} as a single fraction.

$$x\leq \frac{107}{25\left(-4\right)}$$

Multiply 25 and -4 to get -100.

$$x\leq \frac{107}{-100}$$

Fraction \frac{107}{-100} can be rewritten as -\frac{107}{100} by extracting the negative sign.

$$x\leq -\frac{107}{100}$$