Solve -x+1/2-1<x+32/5

$$\frac { - x + 1 } { 2 } - 1 < \frac { x + 32 } { 5 }$$

Solve for x

$$x>-\frac{69}{7}$$

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.

$$5\left(-x+1\right)-10<2\left(x+32\right)$$

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

$$5\left(-x\right)+5-10<2\left(x+32\right)$$

Subtract 10 from 5 to get -5.

$$5\left(-x\right)-5<2\left(x+32\right)$$

Use the distributive property to multiply 2 by x+32.

$$5\left(-x\right)-5<2x+64$$

Subtract 2x from both sides.

$$5\left(-x\right)-5-2x<64$$

Add 5 to both sides.

$$5\left(-x\right)-2x<64+5$$

Add 64 and 5 to get 69.

$$5\left(-x\right)-2x<69$$

Multiply 5 and -1 to get -5.

$$-5x-2x<69$$

Combine -5x and -2x to get -7x.

$$-7x<69$$

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

$$x>-\frac{69}{7}$$