Pre-Algebra Examples

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

Step 1

Simplify $7 (2 d - 1) + 5 (2 - 3 d)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $2$ by $7$ .

$14 d + 7 \cdot - 1 + 5 (2 - 3 d) = 2 d$

Step 1.1.3

Multiply $7$ by $- 1$ .

$14 d - 7 + 5 (2 - 3 d) = 2 d$

Step 1.1.4

Apply the distributive property.

$14 d - 7 + 5 \cdot 2 + 5 (- 3 d) = 2 d$

Step 1.1.5

Multiply $5$ by $2$ .

$14 d - 7 + 10 + 5 (- 3 d) = 2 d$

Step 1.1.6

Multiply $- 3$ by $5$ .

$14 d - 7 + 10 - 15 d = 2 d$

$14 d - 7 + 10 - 15 d = 2 d$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $15 d$ from $14 d$ .

$- d - 7 + 10 = 2 d$

Step 1.2.2

Add $- 7$ and $10$ .

$- d + 3 = 2 d$

$- d + 3 = 2 d$

$- d + 3 = 2 d$

Step 2

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

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Step 2.1

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

$- d + 3 - 2 d = 0$

Step 2.2

Subtract $2 d$ from $- d$ .

$- 3 d + 3 = 0$

$- 3 d + 3 = 0$

Step 3

Subtract $3$ from both sides of the equation.

$- 3 d = - 3$

Step 4

Divide each term in $- 3 d = - 3$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 d = - 3$ by $- 3$ .

$\frac{- 3 d}{- 3} = \frac{- 3}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 d}{- 3} = \frac{- 3}{- 3}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{- 3}{- 3}$

$d = \frac{- 3}{- 3}$

$d = \frac{- 3}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 3$ by $- 3$ .

$d = 1$

$d = 1$

$d = 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$