Algebra Examples

$6 x (x - 7) < 2 (3 x - 1) (x - 8)$

Step 1

Solve $x < 2$ .

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Step 1.1

Simplify $6 x (x - 7)$ .

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Step 1.1.1

Rewrite.

$0 + 0 + 6 x (x - 7) < 2 (3 x - 1) (x - 8)$

Step 1.1.2

Simplify by adding zeros.

$6 x (x - 7) < 2 (3 x - 1) (x - 8)$

Step 1.1.3

Apply the distributive property.

$6 x \cdot x + 6 x \cdot - 7 < 2 (3 x - 1) (x - 8)$

Step 1.1.4

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

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Step 1.1.4.1

Move $x$ .

$6 (x \cdot x) + 6 x \cdot - 7 < 2 (3 x - 1) (x - 8)$

Step 1.1.4.2

Multiply $x$ by $x$ .

$6 x^{2} + 6 x \cdot - 7 < 2 (3 x - 1) (x - 8)$

Step 1.1.5

Multiply $- 7$ by $6$ .

$6 x^{2} - 42 x < 2 (3 x - 1) (x - 8)$

Step 1.2

Simplify $2 (3 x - 1) (x - 8)$ .

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Step 1.2.1

Simplify by multiplying through.

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Step 1.2.1.1

Apply the distributive property.

$6 x^{2} - 42 x < (2 (3 x) + 2 \cdot - 1) (x - 8)$

Step 1.2.1.2

Multiply.

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Step 1.2.1.2.1

Multiply $3$ by $2$ .

$6 x^{2} - 42 x < (6 x + 2 \cdot - 1) (x - 8)$

Step 1.2.1.2.2

Multiply $2$ by $- 1$ .

$6 x^{2} - 42 x < (6 x - 2) (x - 8)$

Step 1.2.2

Expand $(6 x - 2) (x - 8)$ using the FOIL Method.

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Step 1.2.2.1

Apply the distributive property.

$6 x^{2} - 42 x < 6 x (x - 8) - 2 (x - 8)$

Step 1.2.2.2

Apply the distributive property.

$6 x^{2} - 42 x < 6 x \cdot x + 6 x \cdot - 8 - 2 (x - 8)$

Step 1.2.2.3

Apply the distributive property.

$6 x^{2} - 42 x < 6 x \cdot x + 6 x \cdot - 8 - 2 x - 2 \cdot - 8$

Step 1.2.3

Simplify and combine like terms.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

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

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Step 1.2.3.1.1.1

Move $x$ .

$6 x^{2} - 42 x < 6 (x \cdot x) + 6 x \cdot - 8 - 2 x - 2 \cdot - 8$

Step 1.2.3.1.1.2

Multiply $x$ by $x$ .

$6 x^{2} - 42 x < 6 x^{2} + 6 x \cdot - 8 - 2 x - 2 \cdot - 8$

Step 1.2.3.1.2

Multiply $- 8$ by $6$ .

$6 x^{2} - 42 x < 6 x^{2} - 48 x - 2 x - 2 \cdot - 8$

Step 1.2.3.1.3

Multiply $- 2$ by $- 8$ .

$6 x^{2} - 42 x < 6 x^{2} - 48 x - 2 x + 16$

Step 1.2.3.2

Subtract $2 x$ from $- 48 x$ .

$6 x^{2} - 42 x < 6 x^{2} - 50 x + 16$

Step 1.3

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

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Step 1.3.1

Subtract $6 x^{2}$ from both sides of the inequality.

$6 x^{2} - 42 x - 6 x^{2} < - 50 x + 16$

Step 1.3.2

Add $50 x$ to both sides of the inequality.

$6 x^{2} - 42 x - 6 x^{2} + 50 x < 16$

Step 1.3.3

Combine the opposite terms in $6 x^{2} - 42 x - 6 x^{2} + 50 x$ .

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Step 1.3.3.1

Subtract $6 x^{2}$ from $6 x^{2}$ .

$- 42 x + 0 + 50 x < 16$

Step 1.3.3.2

Add $- 42 x$ and $0$ .

$- 42 x + 50 x < 16$

Step 1.3.4

Add $- 42 x$ and $50 x$ .

$8 x < 16$

Step 1.4

Divide each term in $8 x < 16$ by $8$ and simplify.

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Step 1.4.1

Divide each term in $8 x < 16$ by $8$ .

$\frac{8 x}{8} < \frac{16}{8}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $8$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{8 x}{8} < \frac{16}{8}$

Step 1.4.2.1.2

Divide $x$ by $1$ .

$x < \frac{16}{8}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Divide $16$ by $8$ .

$x < 2$

Step 2

Use the inequality $x < 2$ to build the set notation.

${x | x < 2}$

Step 3