Algebra Examples

$3 (2 d - 1) - 2 d = 4 (d - 2) + 5$

Step 1

Simplify $3 (2 d - 1) - 2 d$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 (2 d) + 3 \cdot - 1 - 2 d = 4 (d - 2) + 5$

Step 1.1.2

Multiply $2$ by $3$ .

$6 d + 3 \cdot - 1 - 2 d = 4 (d - 2) + 5$

Step 1.1.3

Multiply $3$ by $- 1$ .

$6 d - 3 - 2 d = 4 (d - 2) + 5$

Step 1.2

Subtract $2 d$ from $6 d$ .

$4 d - 3 = 4 (d - 2) + 5$

Step 2

Simplify $4 (d - 2) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 d - 3 = 4 d + 4 \cdot - 2 + 5$

Step 2.1.2

Multiply $4$ by $- 2$ .

$4 d - 3 = 4 d - 8 + 5$

Step 2.2

Add $- 8$ and $5$ .

$4 d - 3 = 4 d - 3$

Step 3

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

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Step 3.1

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

$4 d - 3 - 4 d = - 3$

Step 3.2

Combine the opposite terms in $4 d - 3 - 4 d$ .

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Step 3.2.1

Subtract $4 d$ from $4 d$ .

$0 - 3 = - 3$

Step 3.2.2

Subtract $3$ from $0$ .

$- 3 = - 3$

Step 4

Since $- 3 = - 3$ , the equation will always be true.

Always true