Algebra Examples

$\frac{1}{3} (6 x + 12) - 2 (x - 7) = 19$

Step 1

Simplify $\frac{1}{3} \cdot (6 x + 12) - 2 (x - 7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{3} (6 x) + \frac{1}{3} \cdot 12 - 2 (x - 7) = 19$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Factor $3$ out of $6 x$ .

$\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot 12 - 2 (x - 7) = 19$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot 12 - 2 (x - 7) = 19$

Step 1.1.2.3

Rewrite the expression.

$2 x + \frac{1}{3} \cdot 12 - 2 (x - 7) = 19$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Factor $3$ out of $12$ .

$2 x + \frac{1}{3} \cdot (3 (4)) - 2 (x - 7) = 19$

Step 1.1.3.2

Cancel the common factor.

$2 x + \frac{1}{3} \cdot (3 \cdot 4) - 2 (x - 7) = 19$

Step 1.1.3.3

Rewrite the expression.

$2 x + 4 - 2 (x - 7) = 19$

Step 1.1.4

Apply the distributive property.

$2 x + 4 - 2 x - 2 \cdot - 7 = 19$

Step 1.1.5

Multiply $- 2$ by $- 7$ .

$2 x + 4 - 2 x + 14 = 19$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $2 x + 4 - 2 x + 14$ .

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Step 1.2.1.1

Subtract $2 x$ from $2 x$ .

$0 + 4 + 14 = 19$

Step 1.2.1.2

Add $0$ and $4$ .

$4 + 14 = 19$

Step 1.2.2

Add $4$ and $14$ .

$18 = 19$

Step 2

Since $18 \neq 19$ , there are no solutions.

No solution