Solve 5(x-4)+3(x+1)leq2(x-2)

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

Solve for x

$$x\leq \frac{13}{6}$$

Solution Steps

Use the distributive property to multiply 5 by x-4.

$$5x-20+3\left(x+1\right)\leq 2\left(x-2\right)$$

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

$$5x-20+3x+3\leq 2\left(x-2\right)$$

Combine 5x and 3x to get 8x.

$$8x-20+3\leq 2\left(x-2\right)$$

Add -20 and 3 to get -17.

$$8x-17\leq 2\left(x-2\right)$$

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

$$8x-17\leq 2x-4$$

Subtract 2x from both sides.

$$8x-17-2x\leq -4$$

Combine 8x and -2x to get 6x.

$$6x-17\leq -4$$

Add 17 to both sides.

$$6x\leq -4+17$$

Add -4 and 17 to get 13.

$$6x\leq 13$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x\leq \frac{13}{6}$$