Solve 2(x-1)-3(3x+1)geq-6(x-5)

$$2 ( x - 1 ) - 3 ( 3 x + 1 ) \geq - 6 ( x - 5 )$$

Solve for x

$$x\leq -35$$

Solution Steps

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

$$2x-2-3\left(3x+1\right)\geq -6\left(x-5\right)$$

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

$$2x-2-9x-3\geq -6\left(x-5\right)$$

Combine 2x and -9x to get -7x.

$$-7x-2-3\geq -6\left(x-5\right)$$

Subtract 3 from -2 to get -5.

$$-7x-5\geq -6\left(x-5\right)$$

Use the distributive property to multiply -6 by x-5.

$$-7x-5\geq -6x+30$$

Add 6x to both sides.

$$-7x-5+6x\geq 30$$

Combine -7x and 6x to get -x.

$$-x-5\geq 30$$

Add 5 to both sides.

$$-x\geq 30+5$$

Add 30 and 5 to get 35.

$$-x\geq 35$$

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

$$x\leq -35$$