Algebra Examples

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

Step 1

Simplify $2 (2 x - 5)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 5 = 3 (x + 2)$

Step 1.4.2

Multiply $2$ by $- 5$ .

$4 x - 10 = 3 (x + 2)$

Step 2

Simplify $3 (x + 2)$ .

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Step 2.1

Apply the distributive property.

$4 x - 10 = 3 x + 3 \cdot 2$

Step 2.2

Multiply $3$ by $2$ .

$4 x - 10 = 3 x + 6$

Step 3

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

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Step 3.1

Subtract $3 x$ from both sides of the equation.

$4 x - 10 - 3 x = 6$

Step 3.2

Subtract $3 x$ from $4 x$ .

$x - 10 = 6$

Step 4

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

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Step 4.1

Add $10$ to both sides of the equation.

$x = 6 + 10$

Step 4.2

Add $6$ and $10$ .

$x = 16$