Finite Math Examples

$2 (3 x - 15) = 6 (x - 5)$

Step 1

Simplify $2 (3 x - 15)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (3 x - 15) = 6 (x - 5)$

Step 1.2

Simplify by adding zeros.

$2 (3 x - 15) = 6 (x - 5)$

Step 1.3

Apply the distributive property.

$2 (3 x) + 2 \cdot - 15 = 6 (x - 5)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 15 = 6 (x - 5)$

Step 1.4.2

Multiply $2$ by $- 15$ .

$6 x - 30 = 6 (x - 5)$

Step 2

Simplify $6 (x - 5)$ .

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Step 2.1

Apply the distributive property.

$6 x - 30 = 6 x + 6 \cdot - 5$

Step 2.2

Multiply $6$ by $- 5$ .

$6 x - 30 = 6 x - 30$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the equation.

$6 x - 30 - 6 x = - 30$

Step 3.2

Combine the opposite terms in $6 x - 30 - 6 x$ .

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Step 3.2.1

Subtract $6 x$ from $6 x$ .

$0 - 30 = - 30$

Step 3.2.2

Subtract $30$ from $0$ .

$- 30 = - 30$

Step 4

Since $- 30 = - 30$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$