Solve x+3/2geq2x-5/3

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

Solve for x

$$x\leq 19$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

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

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

$$3x+9\geq 2\left(2x-5\right)$$

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

$$3x+9\geq 4x-10$$

Subtract 4x from both sides.

$$3x+9-4x\geq -10$$

Combine 3x and -4x to get -x.

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

Subtract 9 from both sides.

$$-x\geq -10-9$$

Subtract 9 from -10 to get -19.

$$-x\geq -19$$

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

$$x\leq \frac{-19}{-1}$$

Fraction \frac{-19}{-1} can be simplified to 19 by removing the negative sign from both the numerator and the denominator.

$$x\leq 19$$