Pre-Algebra Examples

$4 (x - 6) - 6 (x - 4) = x + 8 - (x - 2)$

Step 1

Simplify $4 (x - 6) - 6 (x - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 x + 4 \cdot - 6 - 6 (x - 4) = x + 8 - (x - 2)$

Step 1.1.2

Multiply $4$ by $- 6$ .

$4 x - 24 - 6 (x - 4) = x + 8 - (x - 2)$

Step 1.1.3

Apply the distributive property.

$4 x - 24 - 6 x - 6 \cdot - 4 = x + 8 - (x - 2)$

Step 1.1.4

Multiply $- 6$ by $- 4$ .

$4 x - 24 - 6 x + 24 = x + 8 - (x - 2)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $4 x - 24 - 6 x + 24$ .

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Step 1.2.1.1

Add $- 24$ and $24$ .

$4 x - 6 x + 0 = x + 8 - (x - 2)$

Step 1.2.1.2

Add $4 x - 6 x$ and $0$ .

$4 x - 6 x = x + 8 - (x - 2)$

Step 1.2.2

Subtract $6 x$ from $4 x$ .

$- 2 x = x + 8 - (x - 2)$

Step 2

Simplify $x + 8 - (x - 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 x = x + 8 - x - - 2$

Step 2.1.2

Multiply $- 1$ by $- 2$ .

$- 2 x = x + 8 - x + 2$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $x + 8 - x + 2$ .

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Step 2.2.1.1

Subtract $x$ from $x$ .

$- 2 x = 0 + 8 + 2$

Step 2.2.1.2

Add $0$ and $8$ .

$- 2 x = 8 + 2$

Step 2.2.2

Add $8$ and $2$ .

$- 2 x = 10$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 5$

Step 4