Pre-Algebra Examples

$1.5 (2 p + 6) = \frac{3}{2} \cdot (4 p + 8)$

Step 1

Simplify $1.5 (2 p + 6)$ .

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Step 1.1

Apply the distributive property.

$1.5 (2 p) + 1.5 \cdot 6 = \frac{3}{2} \cdot (4 p + 8)$

Step 1.2

Multiply.

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Step 1.2.1

Multiply $2$ by $1.5$ .

$3 p + 1.5 \cdot 6 = \frac{3}{2} \cdot (4 p + 8)$

Step 1.2.2

Multiply $1.5$ by $6$ .

$3 p + 9 = \frac{3}{2} \cdot (4 p + 8)$

Step 2

Simplify $\frac{3}{2} \cdot (4 p + 8)$ .

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Step 2.1

Apply the distributive property.

$3 p + 9 = \frac{3}{2} (4 p) + \frac{3}{2} \cdot 8$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $4 p$ .

$3 p + 9 = \frac{3}{2} (2 (2 p)) + \frac{3}{2} \cdot 8$

Step 2.2.2

Cancel the common factor.

$3 p + 9 = \frac{3}{2} (2 (2 p)) + \frac{3}{2} \cdot 8$

Step 2.2.3

Rewrite the expression.

$3 p + 9 = 3 (2 p) + \frac{3}{2} \cdot 8$

Step 2.3

Multiply $2$ by $3$ .

$3 p + 9 = 6 p + \frac{3}{2} \cdot 8$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $8$ .

$3 p + 9 = 6 p + \frac{3}{2} \cdot (2 (4))$

Step 2.4.2

Cancel the common factor.

$3 p + 9 = 6 p + \frac{3}{2} \cdot (2 \cdot 4)$

Step 2.4.3

Rewrite the expression.

$3 p + 9 = 6 p + 3 \cdot 4$

Step 2.5

Multiply $3$ by $4$ .

$3 p + 9 = 6 p + 12$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$p = - 1$

Step 4