Algebra Examples

$3 (\frac{7}{3} x + \frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1

Simplify $3 (\frac{7}{3} x + \frac{4}{3}) - 2 x + 8$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{7}{3}$ and $x$ .

$3 (\frac{7 x}{3} + \frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1.1.2

Apply the distributive property.

$3 \frac{7 x}{3} + 3 (\frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Cancel the common factor.

$3 \frac{7 x}{3} + 3 (\frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1.1.3.2

Rewrite the expression.

$7 x + 3 (\frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Cancel the common factor.

$7 x + 3 (\frac{4}{3}) - 2 x + 8 = 5 x + 12$

Step 1.1.4.2

Rewrite the expression.

$7 x + 4 - 2 x + 8 = 5 x + 12$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 x$ from $7 x$ .

$5 x + 4 + 8 = 5 x + 12$

Step 1.2.2

Add $4$ and $8$ .

$5 x + 12 = 5 x + 12$

Step 2

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

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Step 2.1

Subtract $5 x$ from both sides of the equation.

$5 x + 12 - 5 x = 12$

Step 2.2

Combine the opposite terms in $5 x + 12 - 5 x$ .

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Step 2.2.1

Subtract $5 x$ from $5 x$ .

$0 + 12 = 12$

Step 2.2.2

Add $0$ and $12$ .

$12 = 12$

Step 3

Since $12 = 12$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$