Solve 3-2x+1/5geqx+3/4

$$3 - \frac { 2 x + 1 } { 5 } \geq x + \frac { 3 } { 4 }$$

Solve for x

$$x\leq \frac{41}{28}$$

Solution Steps

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

$$60-4\left(2x+1\right)\geq 20x+15$$

Use the distributive property to multiply -4 by 2x+1.

$$60-8x-4\geq 20x+15$$

Subtract 4 from 60 to get 56.

$$56-8x\geq 20x+15$$

Subtract 20x from both sides.

$$56-8x-20x\geq 15$$

Combine -8x and -20x to get -28x.

$$56-28x\geq 15$$

Subtract 56 from both sides.

$$-28x\geq 15-56$$

Subtract 56 from 15 to get -41.

$$-28x\geq -41$$

Divide both sides by -28. Since -28 is negative, the inequality direction is changed.

$$x\leq \frac{-41}{-28}$$

Fraction \frac{-41}{-28} can be simplified to \frac{41}{28} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{41}{28}$$