Algebra Examples

$5 x - (7 x - 4) - 2 = 5 - (3 x + 2)$

Step 1

Simplify $5 x - (7 x - 4) - 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x - (7 x) - - 4 - 2 = 5 - (3 x + 2)$

Step 1.1.2

Multiply $7$ by $- 1$ .

$5 x - 7 x - - 4 - 2 = 5 - (3 x + 2)$

Step 1.1.3

Multiply $- 1$ by $- 4$ .

$5 x - 7 x + 4 - 2 = 5 - (3 x + 2)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $7 x$ from $5 x$ .

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

Step 1.2.2

Subtract $2$ from $4$ .

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 x + 2 = 5 - (3 x) - 1 \cdot 2$

Step 2.1.2

Multiply $3$ by $- 1$ .

$- 2 x + 2 = 5 - 3 x - 1 \cdot 2$

Step 2.1.3

Multiply $- 1$ by $2$ .

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

Step 2.2

Subtract $2$ from $5$ .

$- 2 x + 2 = - 3 x + 3$

Step 3

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

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Step 3.1

Add $3 x$ to both sides of the equation.

$- 2 x + 2 + 3 x = 3$

Step 3.2

Add $- 2 x$ and $3 x$ .

$x + 2 = 3$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$x = 3 - 2$

Step 4.2

Subtract $2$ from $3$ .

$x = 1$