Solve the Inequality for p 2p(5p+2)-p(10p+3)<=14

$2 p (5 p + 2) - p (10 p + 3) \leq 14$

Simplify each term.

Apply the distributive property.

$2 p (5 p) + 2 p \cdot 2 - p (10 p + 3) \leq 14$

Rewrite using the commutative property of multiplication.

$2 \cdot 5 p \cdot p + 2 p \cdot 2 - p (10 p + 3) \leq 14$

Multiply $2$ by $2$ .

$2 \cdot 5 p \cdot p + 4 p - p (10 p + 3) \leq 14$

Simplify each term.

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$2 \cdot 5 (p \cdot p) + 4 p - p (10 p + 3) \leq 14$

Multiply $p$ by $p$ .

$2 \cdot 5 p^{2} + 4 p - p (10 p + 3) \leq 14$

Multiply $2$ by $5$ .

$10 p^{2} + 4 p - p (10 p + 3) \leq 14$

Apply the distributive property.

$10 p^{2} + 4 p - p (10 p) - p \cdot 3 \leq 14$

Rewrite using the commutative property of multiplication.

$10 p^{2} + 4 p - 1 \cdot 10 p \cdot p - p \cdot 3 \leq 14$

Multiply $3$ by $- 1$ .

$10 p^{2} + 4 p - 1 \cdot 10 p \cdot p - 3 p \leq 14$

Simplify each term.

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$10 p^{2} + 4 p - 1 \cdot 10 (p \cdot p) - 3 p \leq 14$

Multiply $p$ by $p$ .

$10 p^{2} + 4 p - 1 \cdot 10 p^{2} - 3 p \leq 14$

Multiply $- 1$ by $10$ .

$10 p^{2} + 4 p - 10 p^{2} - 3 p \leq 14$

Simplify by adding terms.

Combine the opposite terms in $10 p^{2} + 4 p - 10 p^{2} - 3 p$ .

Subtract $10 p^{2}$ from $10 p^{2}$ .

$4 p + 0 - 3 p \leq 14$

Add $4 p$ and $0$ .

$4 p - 3 p \leq 14$

Subtract $3 p$ from $4 p$ .

$p \leq 14$

The result can be shown in multiple forms.

Inequality Form:

$p \leq 14$

Interval Notation:

$(- \infty, 14]$