Precalculus Examples

$5 + 4 (w - 1) = 2 w + 2 (w + 4)$

Step 1

Since $w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 w + 2 (w + 4) = 5 + 4 (w - 1)$

Step 2

Simplify $2 w + 2 (w + 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 w + 2 w + 2 \cdot 4 = 5 + 4 (w - 1)$

Step 2.1.2

Multiply $2$ by $4$ .

$2 w + 2 w + 8 = 5 + 4 (w - 1)$

Step 2.2

Add $2 w$ and $2 w$ .

$4 w + 8 = 5 + 4 (w - 1)$

Step 3

Simplify $5 + 4 (w - 1)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$4 w + 8 = 5 + 4 w + 4 \cdot - 1$

Step 3.1.2

Multiply $4$ by $- 1$ .

$4 w + 8 = 5 + 4 w - 4$

Step 3.2

Subtract $4$ from $5$ .

$4 w + 8 = 4 w + 1$

Step 4

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

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Step 4.1

Subtract $4 w$ from both sides of the equation.

$4 w + 8 - 4 w = 1$

Step 4.2

Combine the opposite terms in $4 w + 8 - 4 w$ .

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Step 4.2.1

Subtract $4 w$ from $4 w$ .

$0 + 8 = 1$

Step 4.2.2

Add $0$ and $8$ .

$8 = 1$

Step 5

Since $8 \neq 1$ , there are no solutions.

No solution