Solve 3p-8+2pleq2(p-3)+1

$$3 p - 8 + 2 p \leq 2 ( p - 3 ) + 1$$

Solve for p

$$p\leq 1$$

Solution Steps

Combine 3p and 2p to get 5p.

$$5p-8\leq 2\left(p-3\right)+1$$

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

$$5p-8\leq 2p-6+1$$

Add -6 and 1 to get -5.

$$5p-8\leq 2p-5$$

Subtract 2p from both sides.

$$5p-8-2p\leq -5$$

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

$$3p-8\leq -5$$

Add 8 to both sides.

$$3p\leq -5+8$$

Add -5 and 8 to get 3.

$$3p\leq 3$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$p\leq \frac{3}{3}$$

Divide 3 by 3 to get 1.

$$p\leq 1$$