Basic Math Examples

- 7 (- 3 c + 5) - 5 c = 6 (c - 3) - 2

$- 7 (- 3 c + 5) - 5 c = 6 (c - 3) - 2$

Step 1

Simplify

- 7 (- 3 c + 5) - 5 c

$- 7 (- 3 c + 5) - 5 c$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

- 7 (- 3 c) - 7 \cdot 5 - 5 c = 6 (c - 3) - 2

$- 7 (- 3 c) - 7 \cdot 5 - 5 c = 6 (c - 3) - 2$

Step 1.1.2

Multiply

- 3

$- 3$ by

- 7

$- 7$ .

21 c - 7 \cdot 5 - 5 c = 6 (c - 3) - 2

$21 c - 7 \cdot 5 - 5 c = 6 (c - 3) - 2$

Step 1.1.3

Multiply

- 7

$- 7$ by

$5$ .

$21 c - 35 - 5 c = 6 (c - 3) - 2$

$21 c - 35 - 5 c = 6 (c - 3) - 2$

Step 1.2

Subtract

$5 c$ from

$21 c$ .

$16 c - 35 = 6 (c - 3) - 2$

$16 c - 35 = 6 (c - 3) - 2$

Step 2

Simplify

$6 (c - 3) - 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$16 c - 35 = 6 c + 6 \cdot - 3 - 2$

Step 2.1.2

Multiply

$6$ by

$- 3$ .

$16 c - 35 = 6 c - 18 - 2$

$16 c - 35 = 6 c - 18 - 2$

Step 2.2

Subtract

$2$ from

$- 18$ .

$16 c - 35 = 6 c - 20$

$16 c - 35 = 6 c - 20$

Step 3

Move all terms containing

$c$ to the left side of the equation.

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Step 3.1

Subtract

$6 c$ from both sides of the equation.

$16 c - 35 - 6 c = - 20$

Step 3.2

Subtract

$6 c$ from

$16 c$ .

$10 c - 35 = - 20$

$10 c - 35 = - 20$

Step 4

Move all terms not containing

$c$ to the right side of the equation.

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Step 4.1

Add

$35$ to both sides of the equation.

$10 c = - 20 + 35$

Step 4.2

Add

$- 20$ and

$35$ .

$10 c = 15$

$10 c = 15$

Step 5

Divide each term in

$10 c = 15$ by

$10$ and simplify.

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Step 5.1

Divide each term in

$10 c = 15$ by

$10$ .

$\frac{10 c}{10} = \frac{15}{10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of

$10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{10 c}{10} = \frac{15}{10}$

Step 5.2.1.2

Divide

$c$ by

$1$ .

$c = \frac{15}{10}$

$c = \frac{15}{10}$

$c = \frac{15}{10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of

$15$ and

$10$ .

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Step 5.3.1.1

Factor

$5$ out of

$15$ .

$c = \frac{5 (3)}{10}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor

$5$ out of

$10$ .

$c = \frac{5 \cdot 3}{5 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$c = \frac{5 \cdot 3}{5 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$c = \frac{3}{2}$

$c = \frac{3}{2}$

$c = \frac{3}{2}$

$c = \frac{3}{2}$

$c = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \frac{3}{2}$

Decimal Form:

$c = 1.5$

Mixed Number Form:

$c = 1 \frac{1}{2}$

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