Linear Algebra Examples

$3 (x + 1) = 7 - 2 x$

Step 1

Simplify $3 (x + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (x + 1) = 7 - 2 x$

Step 1.2

Simplify by adding zeros.

$3 (x + 1) = 7 - 2 x$

Step 1.3

Apply the distributive property.

$3 x + 3 \cdot 1 = 7 - 2 x$

Step 1.4

Multiply $3$ by $1$ .

$3 x + 3 = 7 - 2 x$

Step 2

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

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Step 2.1

Add $2 x$ to both sides of the equation.

$3 x + 3 + 2 x = 7$

Step 2.2

Add $3 x$ and $2 x$ .

$5 x + 3 = 7$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$5 x = 7 - 3$

Step 3.2

Subtract $3$ from $7$ .

$5 x = 4$

Step 4

Divide each term in $5 x = 4$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 5

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

${x | x = \frac{4}{5}}$

Step 6