Finite Math Examples

$- 7 (\frac{1}{7} y - 1) + y = 7$

Step 1

Simplify $- 7 (\frac{1}{7} y - 1) + y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{7}$ and $y$ .

$- 7 (\frac{y}{7} - 1) + y = 7$

Step 1.1.2

Apply the distributive property.

$- 7 \frac{y}{7} - 7 \cdot - 1 + y = 7$

Step 1.1.3

Cancel the common factor of $7$ .

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Step 1.1.3.1

Factor $7$ out of $- 7$ .

$7 (- 1) \frac{y}{7} - 7 \cdot - 1 + y = 7$

Step 1.1.3.2

Cancel the common factor.

$7 \cdot - 1 \frac{y}{7} - 7 \cdot - 1 + y = 7$

Step 1.1.3.3

Rewrite the expression.

$- 1 y - 7 \cdot - 1 + y = 7$

$- 1 y - 7 \cdot - 1 + y = 7$

Step 1.1.4

Multiply $- 7$ by $- 1$ .

$- 1 y + 7 + y = 7$

Step 1.1.5

Rewrite $- 1 y$ as $- y$ .

$- y + 7 + y = 7$

$- y + 7 + y = 7$

Step 1.2

Combine the opposite terms in $- y + 7 + y$ .

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Step 1.2.1

Add $- y$ and $y$ .

$0 + 7 = 7$

Step 1.2.2

Add $0$ and $7$ .

$7 = 7$

$7 = 7$

$7 = 7$

Step 2

Since $7 = 7$ , the equation will always be true for any value of $y$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

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