Solve 2(x+5)-4>-5(x-5)+9

$$2 ( x + 5 ) - 4 > - 5 ( x - 5 ) + 9$$

Solve for x

$$x>4$$

Solution Steps

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

$$2x+10-4>-5\left(x-5\right)+9$$

Subtract 4 from 10 to get 6.

$$2x+6>-5\left(x-5\right)+9$$

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

$$2x+6>-5x+25+9$$

Add 25 and 9 to get 34.

$$2x+6>-5x+34$$

Add 5x to both sides.

$$2x+6+5x>34$$

Combine 2x and 5x to get 7x.

$$7x+6>34$$

Subtract 6 from both sides.

$$7x>34-6$$

Subtract 6 from 34 to get 28.

$$7x>28$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x>\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$x>4$$