Solve 5(2x+3)<3(7x-2)+5

$$5 ( 2 x + 3 ) < 3 ( 7 x - 2 ) + 5$$

Solve for x

$$x>\frac{16}{11}$$

Solution Steps

Use the distributive property to multiply 5 by 2x+3.

$$10x+15<3\left(7x-2\right)+5$$

Use the distributive property to multiply 3 by 7x-2.

$$10x+15<21x-6+5$$

Add -6 and 5 to get -1.

$$10x+15<21x-1$$

Subtract 21x from both sides.

$$10x+15-21x<-1$$

Combine 10x and -21x to get -11x.

$$-11x+15<-1$$

Subtract 15 from both sides.

$$-11x<-1-15$$

Subtract 15 from -1 to get -16.

$$-11x<-16$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x>\frac{-16}{-11}$$

Fraction \frac{-16}{-11} can be simplified to \frac{16}{11} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{16}{11}$$