Solve 3x+2/5geq2x-5/3+1

$$\frac { 3 x + 2 } { 5 } \geq \frac { 2 x - 5 } { 3 } + 1$$

Solve for x

$$x\leq 16$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

$$3\left(3x+2\right)\geq 5\left(2x-5\right)+15$$

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

$$9x+6\geq 5\left(2x-5\right)+15$$

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

$$9x+6\geq 10x-25+15$$

Add -25 and 15 to get -10.

$$9x+6\geq 10x-10$$

Subtract 10x from both sides.

$$9x+6-10x\geq -10$$

Combine 9x and -10x to get -x.

$$-x+6\geq -10$$

Subtract 6 from both sides.

$$-x\geq -10-6$$

Subtract 6 from -10 to get -16.

$$-x\geq -16$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq \frac{-16}{-1}$$

Fraction \frac{-16}{-1} can be simplified to 16 by removing the negative sign from both the numerator and the denominator.

$$x\leq 16$$