Trigonometry Examples

$3 (x - 1) + 7 = 2 (x + 5)$

Step 1

Simplify $3 (x - 1) + 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 x + 3 \cdot - 1 + 7 = 2 (x + 5)$

Step 1.1.2

Multiply $3$ by $- 1$ .

$3 x - 3 + 7 = 2 (x + 5)$

Step 1.2

Add $- 3$ and $7$ .

$3 x + 4 = 2 (x + 5)$

Step 2

Simplify $2 (x + 5)$ .

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Step 2.1

Apply the distributive property.

$3 x + 4 = 2 x + 2 \cdot 5$

Step 2.2

Multiply $2$ by $5$ .

$3 x + 4 = 2 x + 10$

Step 3

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

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$3 x + 4 - 2 x = 10$

Step 3.2

Subtract $2 x$ from $3 x$ .

$x + 4 = 10$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$x = 10 - 4$

Step 4.2

Subtract $4$ from $10$ .

$x = 6$