Solve the Inequality for x (12x-1)(3x+1)<1+(6x+2)^2

$(12 x - 1) (3 x + 1) < 1 + {(6 x + 2)}^{2}$

Simplify $(12 x - 1) (3 x + 1)$ .

Rewrite.

$0 + 0 + (12 x - 1) (3 x + 1) < 1 + {(6 x + 2)}^{2}$

Simplify by adding zeros.

$(12 x - 1) (3 x + 1) < 1 + {(6 x + 2)}^{2}$

Expand $(12 x - 1) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$12 x (3 x + 1) - 1 (3 x + 1) < 1 + {(6 x + 2)}^{2}$

Apply the distributive property.

$12 x (3 x) + 12 x \cdot 1 - 1 (3 x + 1) < 1 + {(6 x + 2)}^{2}$

Apply the distributive property.

$12 x (3 x) + 12 x \cdot 1 - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$12 \cdot 3 x \cdot x + 12 x \cdot 1 - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$12 \cdot 3 (x \cdot x) + 12 x \cdot 1 - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $x$ by $x$ .

$12 \cdot 3 x^{2} + 12 x \cdot 1 - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $12$ by $3$ .

$36 x^{2} + 12 x \cdot 1 - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $12$ by $1$ .

$36 x^{2} + 12 x - 1 (3 x) - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $3$ by $- 1$ .

$36 x^{2} + 12 x - 3 x - 1 \cdot 1 < 1 + {(6 x + 2)}^{2}$

Multiply $- 1$ by $1$ .

$36 x^{2} + 12 x - 3 x - 1 < 1 + {(6 x + 2)}^{2}$

Subtract $3 x$ from $12 x$ .

$36 x^{2} + 9 x - 1 < 1 + {(6 x + 2)}^{2}$

Simplify $1 + {(6 x + 2)}^{2}$ .

Simplify each term.

Rewrite ${(6 x + 2)}^{2}$ as $(6 x + 2) (6 x + 2)$ .

$36 x^{2} + 9 x - 1 < 1 + (6 x + 2) (6 x + 2)$

Expand $(6 x + 2) (6 x + 2)$ using the FOIL Method.

Apply the distributive property.

$36 x^{2} + 9 x - 1 < 1 + 6 x (6 x + 2) + 2 (6 x + 2)$

Apply the distributive property.

$36 x^{2} + 9 x - 1 < 1 + 6 x (6 x) + 6 x \cdot 2 + 2 (6 x + 2)$

Apply the distributive property.

$36 x^{2} + 9 x - 1 < 1 + 6 x (6 x) + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$36 x^{2} + 9 x - 1 < 1 + 6 \cdot 6 x \cdot x + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$36 x^{2} + 9 x - 1 < 1 + 6 \cdot 6 (x \cdot x) + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $x$ by $x$ .

$36 x^{2} + 9 x - 1 < 1 + 6 \cdot 6 x^{2} + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $6$ by $6$ .

$36 x^{2} + 9 x - 1 < 1 + 36 x^{2} + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $2$ by $6$ .

$36 x^{2} + 9 x - 1 < 1 + 36 x^{2} + 12 x + 2 (6 x) + 2 \cdot 2$

Multiply $6$ by $2$ .

$36 x^{2} + 9 x - 1 < 1 + 36 x^{2} + 12 x + 12 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$36 x^{2} + 9 x - 1 < 1 + 36 x^{2} + 12 x + 12 x + 4$

Add $12 x$ and $12 x$ .

$36 x^{2} + 9 x - 1 < 1 + 36 x^{2} + 24 x + 4$

Add $1$ and $4$ .

$36 x^{2} + 9 x - 1 < 36 x^{2} + 24 x + 5$

Move all terms containing $x$ to the left side of the inequality.

Subtract $36 x^{2}$ from both sides of the inequality.

$36 x^{2} + 9 x - 1 - 36 x^{2} < 24 x + 5$

Subtract $24 x$ from both sides of the inequality.

$36 x^{2} + 9 x - 1 - 36 x^{2} - 24 x < 5$

Combine the opposite terms in $36 x^{2} + 9 x - 1 - 36 x^{2} - 24 x$ .

Subtract $36 x^{2}$ from $36 x^{2}$ .

$9 x - 1 + 0 - 24 x < 5$

Add $9 x - 1$ and $0$ .

$9 x - 1 - 24 x < 5$

Subtract $24 x$ from $9 x$ .

$- 15 x - 1 < 5$

Move all terms not containing $x$ to the right side of the inequality.

Add $1$ to both sides of the inequality.

$- 15 x < 5 + 1$

Add $5$ and $1$ .

$- 15 x < 6$

Divide each term in $- 15 x < 6$ by $- 15$ and simplify.

Divide each term in $- 15 x < 6$ by $- 15$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 15 x}{- 15} > \frac{6}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} > \frac{6}{- 15}$

Divide $x$ by $1$ .

$x > \frac{6}{- 15}$

Simplify the right side.

Cancel the common factor of $6$ and $- 15$ .

Factor $3$ out of $6$ .

$x > \frac{3 (2)}{- 15}$

Cancel the common factors.

Factor $3$ out of $- 15$ .

$x > \frac{3 \cdot 2}{3 \cdot - 5}$

Cancel the common factor.

$x > \frac{3 \cdot 2}{3 \cdot - 5}$

Rewrite the expression.

$x > \frac{2}{- 5}$

Move the negative in front of the fraction.

$x > - \frac{2}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{2}{5}$

Interval Notation:

$(- \frac{2}{5}, \infty)$

Solve the Inequality for x (12x-1)(3x+1)<1+(6x+2)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.