Convert to Set Notation x(36x+23)<=(6x+2)^2

$x (36 x + 23) \leq {(6 x + 2)}^{2}$

Step 1

Solve $x \geq - 4$ .

Simplify $x (36 x + 23)$ .

Rewrite.

$0 + 0 + x (36 x + 23) \leq {(6 x + 2)}^{2}$

Simplify by multiplying through.

Apply the distributive property.

$x (36 x) + x \cdot 23 \leq {(6 x + 2)}^{2}$

Reorder.

Rewrite using the commutative property of multiplication.

$36 x \cdot x + x \cdot 23 \leq {(6 x + 2)}^{2}$

Move $23$ to the left of $x$ .

$36 x \cdot x + 23 \cdot x \leq {(6 x + 2)}^{2}$

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

Move $x$ .

$36 (x \cdot x) + 23 \cdot x \leq {(6 x + 2)}^{2}$

Multiply $x$ by $x$ .

$36 x^{2} + 23 \cdot x \leq {(6 x + 2)}^{2}$

$36 x^{2} + 23 x \leq {(6 x + 2)}^{2}$

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

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

$36 x^{2} + 23 x \leq (6 x + 2) (6 x + 2)$

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

Apply the distributive property.

$36 x^{2} + 23 x \leq 6 x (6 x + 2) + 2 (6 x + 2)$

Apply the distributive property.

$36 x^{2} + 23 x \leq 6 x (6 x) + 6 x \cdot 2 + 2 (6 x + 2)$

Apply the distributive property.

$36 x^{2} + 23 x \leq 6 x (6 x) + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$36 x^{2} + 23 x \leq 6 \cdot 6 x \cdot x + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

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

Move $x$ .

$36 x^{2} + 23 x \leq 6 \cdot 6 (x \cdot x) + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $x$ by $x$ .

$36 x^{2} + 23 x \leq 6 \cdot 6 x^{2} + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $6$ by $6$ .

$36 x^{2} + 23 x \leq 36 x^{2} + 6 x \cdot 2 + 2 (6 x) + 2 \cdot 2$

Multiply $2$ by $6$ .

$36 x^{2} + 23 x \leq 36 x^{2} + 12 x + 2 (6 x) + 2 \cdot 2$

Multiply $6$ by $2$ .

$36 x^{2} + 23 x \leq 36 x^{2} + 12 x + 12 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$36 x^{2} + 23 x \leq 36 x^{2} + 12 x + 12 x + 4$

Add $12 x$ and $12 x$ .

$36 x^{2} + 23 x \leq 36 x^{2} + 24 x + 4$

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

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

$36 x^{2} + 23 x - 36 x^{2} \leq 24 x + 4$

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

$36 x^{2} + 23 x - 36 x^{2} - 24 x \leq 4$

Combine the opposite terms in $36 x^{2} + 23 x - 36 x^{2} - 24 x$ .

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

$23 x + 0 - 24 x \leq 4$

Add $23 x$ and $0$ .

$23 x - 24 x \leq 4$

Subtract $24 x$ from $23 x$ .

$- x \leq 4$

Divide each term in $- x \leq 4$ by $- 1$ and simplify.

Divide each term in $- x \leq 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{4}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$x \geq - 4$

Step 2

Use the inequality $x \geq - 4$ to build the set notation.

${x | x \geq - 4}$

Step 3

Convert to Set Notation x(36x+23)<=(6x+2)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.