Solve 3(5x+4)-2(3x+1)geq2(2x-3)

$$3 ( 5 x + 4 ) - 2 ( 3 x + 1 ) \geq 2 ( 2 x - 3 )$$

Solve for x

$$x\geq -\frac{16}{5}$$

Solution Steps

Use the distributive property to multiply 3 by 5x+4.

$$15x+12-2\left(3x+1\right)\geq 2\left(2x-3\right)$$

Use the distributive property to multiply -2 by 3x+1.

$$15x+12-6x-2\geq 2\left(2x-3\right)$$

Combine 15x and -6x to get 9x.

$$9x+12-2\geq 2\left(2x-3\right)$$

Subtract 2 from 12 to get 10.

$$9x+10\geq 2\left(2x-3\right)$$

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

$$9x+10\geq 4x-6$$

Subtract 4x from both sides.

$$9x+10-4x\geq -6$$

Combine 9x and -4x to get 5x.

$$5x+10\geq -6$$

Subtract 10 from both sides.

$$5x\geq -6-10$$

Subtract 10 from -6 to get -16.

$$5x\geq -16$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\geq -\frac{16}{5}$$