Trigonometry Examples

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

Step 1

Rewrite the equation as $3 (x - 5) - 5 x = - 7$ .

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

Step 2

Simplify $3 (x - 5) - 5 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 x + 3 \cdot - 5 - 5 x = - 7$

Step 2.1.2

Multiply $3$ by $- 5$ .

$3 x - 15 - 5 x = - 7$

Step 2.2

Subtract $5 x$ from $3 x$ .

$- 2 x - 15 = - 7$

Step 3

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

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Step 3.1

Add $15$ to both sides of the equation.

$- 2 x = - 7 + 15$

Step 3.2

Add $- 7$ and $15$ .

$- 2 x = 8$

Step 4

Divide each term in $- 2 x = 8$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x = 8$ by $- 2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $8$ by $- 2$ .

$x = - 4$