Precalculus Examples

$6 (x - (2 x + 3)) = 8 - 5 x$

Step 1

Simplify $6 (x - (2 x + 3))$ .

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Step 1.1

Rewrite.

$0 + 0 + 6 (x - (2 x + 3)) = 8 - 5 x$

Step 1.2

Simplify by adding zeros.

$6 (x - (2 x + 3)) = 8 - 5 x$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$6 (x - (2 x) - 1 \cdot 3) = 8 - 5 x$

Step 1.3.2

Multiply $2$ by $- 1$ .

$6 (x - 2 x - 1 \cdot 3) = 8 - 5 x$

Step 1.3.3

Multiply $- 1$ by $3$ .

$6 (x - 2 x - 3) = 8 - 5 x$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $2 x$ from $x$ .

$6 (- x - 3) = 8 - 5 x$

Step 1.4.2

Apply the distributive property.

$6 (- x) + 6 \cdot - 3 = 8 - 5 x$

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $- 1$ by $6$ .

$- 6 x + 6 \cdot - 3 = 8 - 5 x$

Step 1.4.3.2

Multiply $6$ by $- 3$ .

$- 6 x - 18 = 8 - 5 x$

Step 2

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

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Step 2.1

Add $5 x$ to both sides of the equation.

$- 6 x - 18 + 5 x = 8$

Step 2.2

Add $- 6 x$ and $5 x$ .

$- x - 18 = 8$

Step 3

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

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Step 3.1

Add $18$ to both sides of the equation.

$- x = 8 + 18$

Step 3.2

Add $8$ and $18$ .

$- x = 26$

Step 4

Divide each term in $- x = 26$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x = 26$ by $- 1$ .

$\frac{- x}{- 1} = \frac{26}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{26}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{26}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $26$ by $- 1$ .

$x = - 26$