Solve 2(x-3)/5+1/10<3(3-2x)/2

$$\frac { 2 ( x - 3 ) } { 5 } + \frac { 1 } { 10 } < \frac { 3 ( 3 - 2 x ) } { 2 }$$

Solve for x

$$x<\frac{28}{17}$$

Solution Steps

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

$$2\times 2\left(x-3\right)+1<5\times 3\left(3-2x\right)$$

Multiply 2 and 2 to get 4.

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

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

$$4x-12+1<5\times 3\left(3-2x\right)$$

Add -12 and 1 to get -11.

$$4x-11<5\times 3\left(3-2x\right)$$

Multiply 5 and 3 to get 15.

$$4x-11<15\left(3-2x\right)$$

Use the distributive property to multiply 15 by 3-2x.

$$4x-11<45-30x$$

Add 30x to both sides.

$$4x-11+30x<45$$

Combine 4x and 30x to get 34x.

$$34x-11<45$$

Add 11 to both sides.

$$34x<45+11$$

Add 45 and 11 to get 56.

$$34x<56$$

Divide both sides by 34. Since 34 is positive, the inequality direction remains the same.

$$x<\frac{56}{34}$$

Reduce the fraction \frac{56}{34} to lowest terms by extracting and canceling out 2.

$$x<\frac{28}{17}$$