Algebra Examples

$5 (3 x + 9) - 2 x = 15 x - 2 (x - 5)$

Step 1

Simplify $5 (3 x + 9) - 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 (3 x) + 5 \cdot 9 - 2 x = 15 x - 2 (x - 5)$

Step 1.1.2

Multiply $3$ by $5$ .

$15 x + 5 \cdot 9 - 2 x = 15 x - 2 (x - 5)$

Step 1.1.3

Multiply $5$ by $9$ .

$15 x + 45 - 2 x = 15 x - 2 (x - 5)$

Step 1.2

Subtract $2 x$ from $15 x$ .

$13 x + 45 = 15 x - 2 (x - 5)$

Step 2

Simplify $15 x - 2 (x - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$13 x + 45 = 15 x - 2 x - 2 \cdot - 5$

Step 2.1.2

Multiply $- 2$ by $- 5$ .

$13 x + 45 = 15 x - 2 x + 10$

Step 2.2

Subtract $2 x$ from $15 x$ .

$13 x + 45 = 13 x + 10$

Step 3

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

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Step 3.1

Subtract $13 x$ from both sides of the equation.

$13 x + 45 - 13 x = 10$

Step 3.2

Combine the opposite terms in $13 x + 45 - 13 x$ .

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Step 3.2.1

Subtract $13 x$ from $13 x$ .

$0 + 45 = 10$

Step 3.2.2

Add $0$ and $45$ .

$45 = 10$

Step 4

Since $45 \neq 10$ , there are no solutions.

No solution