Linear Algebra Examples

$\frac{2 x \cdot 4}{3} - 2 = 160$

Step 1

Multiply $4$ by $2$ .

$\frac{8 x}{3} - 2 = 160$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $2$ to both sides of the equation.

$\frac{8 x}{3} = 160 + 2$

Step 2.2

Add $160$ and $2$ .

$\frac{8 x}{3} = 162$

Step 3

Multiply both sides of the equation by $\frac{3}{8}$ .

$\frac{3}{8} \cdot \frac{8 x}{3} = \frac{3}{8} \cdot 162$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{8} \cdot \frac{8 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8 x}{3} = \frac{3}{8} \cdot 162$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 x) = \frac{3}{8} \cdot 162$

Step 4.1.1.2

Cancel the common factor of $8$ .

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Step 4.1.1.2.1

Factor $8$ out of $8 x$ .

$\frac{1}{8} (8 (x)) = \frac{3}{8} \cdot 162$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 x) = \frac{3}{8} \cdot 162$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{3}{8} \cdot 162$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{8} \cdot 162$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $8$ .

$x = \frac{3}{2 (4)} \cdot 162$

Step 4.2.1.1.2

Factor $2$ out of $162$ .

$x = \frac{3}{2 \cdot 4} \cdot (2 \cdot 81)$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{3}{2 \cdot 4} \cdot (2 \cdot 81)$

Step 4.2.1.1.4

Rewrite the expression.

$x = \frac{3}{4} \cdot 81$

Step 4.2.1.2

Combine $\frac{3}{4}$ and $81$ .

$x = \frac{3 \cdot 81}{4}$

Step 4.2.1.3

Multiply $3$ by $81$ .

$x = \frac{243}{4}$

Step 5

The domain is the set of all valid $x$ values.

${x | x = \frac{243}{4}}$

Step 6