Solve 10-3(x-2)leq2(x+1)

$$10 - 3 ( x - 2 ) \leq 2 ( x + 1 )$$

Solve for x

$$x\geq \frac{14}{5}$$

Solution Steps

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

$$10-3x+6\leq 2\left(x+1\right)$$

Add 10 and 6 to get 16.

$$16-3x\leq 2\left(x+1\right)$$

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

$$16-3x\leq 2x+2$$

Subtract 2x from both sides.

$$16-3x-2x\leq 2$$

Combine -3x and -2x to get -5x.

$$16-5x\leq 2$$

Subtract 16 from both sides.

$$-5x\leq 2-16$$

Subtract 16 from 2 to get -14.

$$-5x\leq -14$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-14}{-5}$$

Fraction \frac{-14}{-5} can be simplified to \frac{14}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{14}{5}$$