Basic Math Examples

$3 p - 1 = 5 (p - 1) - 2 (7 - 2 p)$

Step 1

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

$5 (p - 1) - 2 (7 - 2 p) = 3 p - 1$

Step 2

Simplify $5 (p - 1) - 2 (7 - 2 p)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $5$ by $- 1$ .

$5 p - 5 - 2 (7 - 2 p) = 3 p - 1$

Step 2.1.3

Apply the distributive property.

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

Step 2.1.4

Multiply $- 2$ by $7$ .

$5 p - 5 - 14 - 2 (- 2 p) = 3 p - 1$

Step 2.1.5

Multiply $- 2$ by $- 2$ .

$5 p - 5 - 14 + 4 p = 3 p - 1$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $5 p$ and $4 p$ .

$9 p - 5 - 14 = 3 p - 1$

Step 2.2.2

Subtract $14$ from $- 5$ .

$9 p - 19 = 3 p - 1$

Step 3

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

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Step 3.1

Subtract $3 p$ from both sides of the equation.

$9 p - 19 - 3 p = - 1$

Step 3.2

Subtract $3 p$ from $9 p$ .

$6 p - 19 = - 1$

Step 4

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

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Step 4.1

Add $19$ to both sides of the equation.

$6 p = - 1 + 19$

Step 4.2

Add $- 1$ and $19$ .

$6 p = 18$

Step 5

Divide each term in $6 p = 18$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 p = 18$ by $6$ .

$\frac{6 p}{6} = \frac{18}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 p}{6} = \frac{18}{6}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{18}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $18$ by $6$ .

$p = 3$