Solve 3-x/2-(x-1)leq5+x/4

$$\frac { 3 - x } { 2 } - ( x - 1 ) \leq \frac { 5 + x } { 4 }$$

Solve for x

$$x\geq \frac{5}{7}$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4. Since 4 is positive, the inequality direction remains the same.

$$2\left(3-x\right)-4\left(x-1\right)\leq 5+x$$

Use the distributive property to multiply 2 by 3-x.

$$6-2x-4\left(x-1\right)\leq 5+x$$

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

$$6-2x-4x+4\leq 5+x$$

Combine -2x and -4x to get -6x.

$$6-6x+4\leq 5+x$$

Add 6 and 4 to get 10.

$$10-6x\leq 5+x$$

Subtract x from both sides.

$$10-6x-x\leq 5$$

Combine -6x and -x to get -7x.

$$10-7x\leq 5$$

Subtract 10 from both sides.

$$-7x\leq 5-10$$

Subtract 10 from 5 to get -5.

$$-7x\leq -5$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

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

Fraction \frac{-5}{-7} can be simplified to \frac{5}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{5}{7}$$