Solve 5-2x/4geq7x/5

$$\frac { 5 - 2 x } { 4 } \geq \frac { 7 x } { 5 }$$

Solve for x

$$x\leq \frac{25}{38}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,5. Since 20 is positive, the inequality direction remains the same.

$$5\left(5-2x\right)\geq 4\times 7x$$

Use the distributive property to multiply 5 by 5-2x.

$$25-10x\geq 4\times 7x$$

Multiply 4 and 7 to get 28.

$$25-10x\geq 28x$$

Subtract 28x from both sides.

$$25-10x-28x\geq 0$$

Combine -10x and -28x to get -38x.

$$25-38x\geq 0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-38x\geq -25$$

Divide both sides by -38. Since -38 is negative, the inequality direction is changed.

$$x\leq \frac{-25}{-38}$$

Fraction \frac{-25}{-38} can be simplified to \frac{25}{38} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{25}{38}$$