Solve x-5/4leq5x/7

$$\frac { x - 5 } { 4 } \leq \frac { 5 x } { 7 }$$

Solve for x

$$x\geq -\frac{35}{13}$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 4,7. Since 28 is positive, the inequality direction remains the same.

$$7\left(x-5\right)\leq 4\times 5x$$

Use the distributive property to multiply 7 by x-5.

$$7x-35\leq 4\times 5x$$

Multiply 4 and 5 to get 20.

$$7x-35\leq 20x$$

Subtract 20x from both sides.

$$7x-35-20x\leq 0$$

Combine 7x and -20x to get -13x.

$$-13x-35\leq 0$$

Add 35 to both sides. Anything plus zero gives itself.

$$-13x\leq 35$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq -\frac{35}{13}$$