Solve 4(x-5)<3(10-2x)

$$4 ( x - 5 ) < 3 ( 10 - 2 x )$$

Solve for x

$$x<5$$

Solution Steps

Use the distributive property to multiply 4 by x-5.

$$4x-20<3\left(10-2x\right)$$

Use the distributive property to multiply 3 by 10-2x.

$$4x-20<30-6x$$

Add 6x to both sides.

$$4x-20+6x<30$$

Combine 4x and 6x to get 10x.

$$10x-20<30$$

Add 20 to both sides.

$$10x<30+20$$

Add 30 and 20 to get 50.

$$10x<50$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x<\frac{50}{10}$$

Divide 50 by 10 to get 5.

$$x<5$$