Solve 1-x-1/2leq-2(x+3)/5

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

Solve for x

$$x\geq 27$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$10-5\left(x-1\right)\leq 2\left(-2\right)\left(x+3\right)$$

Use the distributive property to multiply -5 by x-1.

$$10-5x+5\leq 2\left(-2\right)\left(x+3\right)$$

Add 10 and 5 to get 15.

$$15-5x\leq 2\left(-2\right)\left(x+3\right)$$

Multiply 2 and -2 to get -4.

$$15-5x\leq -4\left(x+3\right)$$

Use the distributive property to multiply -4 by x+3.

$$15-5x\leq -4x-12$$

Add 4x to both sides.

$$15-5x+4x\leq -12$$

Combine -5x and 4x to get -x.

$$15-x\leq -12$$

Subtract 15 from both sides.

$$-x\leq -12-15$$

Subtract 15 from -12 to get -27.

$$-x\leq -27$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-27}{-1}$$

Fraction \frac{-27}{-1} can be simplified to 27 by removing the negative sign from both the numerator and the denominator.

$$x\geq 27$$