Pre-Algebra Examples

$\frac{4}{3} \cdot (x + 3) + \frac{7}{3} = 6$

Step 1

Simplify $\frac{4}{3} \cdot (x + 3) + \frac{7}{3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{4}{3} x + \frac{4}{3} \cdot 3 + \frac{7}{3} = 6$

Step 1.1.2

Combine $\frac{4}{3}$ and $x$ .

$\frac{4 x}{3} + \frac{4}{3} \cdot 3 + \frac{7}{3} = 6$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Cancel the common factor.

$\frac{4 x}{3} + \frac{4}{3} \cdot 3 + \frac{7}{3} = 6$

Step 1.1.3.2

Rewrite the expression.

$\frac{4 x}{3} + 4 + \frac{7}{3} = 6$

Step 1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x}{3} + 4 \cdot \frac{3}{3} + \frac{7}{3} = 6$

Step 1.3

Combine $4$ and $\frac{3}{3}$ .

$\frac{4 x}{3} + \frac{4 \cdot 3}{3} + \frac{7}{3} = 6$

Step 1.4

Combine the numerators over the common denominator.

$\frac{4 x}{3} + \frac{4 \cdot 3 + 7}{3} = 6$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $3$ .

$\frac{4 x}{3} + \frac{12 + 7}{3} = 6$

Step 1.5.2

Add $12$ and $7$ .

$\frac{4 x}{3} + \frac{19}{3} = 6$

Step 2

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

$x = - \frac{1}{4}$

Step 3