Pre-Algebra Examples

$24 - (4 + 9 x - 4 (x + 5)) = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1

Simplify $24 - (4 + 9 x - 4 (x + 5))$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$24 - (4 + 9 x - 4 x - 4 \cdot 5) = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.1.2

Multiply $- 4$ by $5$ .

$24 - (4 + 9 x - 4 x - 20) = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.2

Subtract $20$ from $4$ .

$24 - (9 x - 4 x - 16) = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.3

Subtract $4 x$ from $9 x$ .

$24 - (5 x - 16) = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.4

Apply the distributive property.

$24 - (5 x) - - 16 = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.5

Multiply $5$ by $- 1$ .

$24 - 5 x - - 16 = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.1.6

Multiply $- 1$ by $- 16$ .

$24 - 5 x + 16 = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 1.2

Add $24$ and $16$ .

$- 5 x + 40 = - 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$

Step 2

Simplify $- 4 (3 x - 3) - (9 (- 1) - 10 x + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 5 x + 40 = - 4 (3 x) - 4 \cdot - 3 - (9 (- 1) - 10 x + 5)$

Step 2.1.2

Multiply $3$ by $- 4$ .

$- 5 x + 40 = - 12 x - 4 \cdot - 3 - (9 (- 1) - 10 x + 5)$

Step 2.1.3

Multiply $- 4$ by $- 3$ .

$- 5 x + 40 = - 12 x + 12 - (9 (- 1) - 10 x + 5)$

Step 2.1.4

Multiply $9$ by $- 1$ .

$- 5 x + 40 = - 12 x + 12 - (- 9 - 10 x + 5)$

Step 2.1.5

Add $- 9$ and $5$ .

$- 5 x + 40 = - 12 x + 12 - (- 10 x - 4)$

Step 2.1.6

Apply the distributive property.

$- 5 x + 40 = - 12 x + 12 - (- 10 x) - - 4$

Step 2.1.7

Multiply $- 10$ by $- 1$ .

$- 5 x + 40 = - 12 x + 12 + 10 x - - 4$

Step 2.1.8

Multiply $- 1$ by $- 4$ .

$- 5 x + 40 = - 12 x + 12 + 10 x + 4$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 12 x$ and $10 x$ .

$- 5 x + 40 = - 2 x + 12 + 4$

Step 2.2.2

Add $12$ and $4$ .

$- 5 x + 40 = - 2 x + 16$

Step 3

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

$x = 8$

Step 4