Basic Math Examples

$2 (y + 2) - 5 (y - 3) = 7 y + 19 - 10 y$

Step 1

Simplify $2 (y + 2) - 5 (y - 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 y + 2 \cdot 2 - 5 (y - 3) = 7 y + 19 - 10 y$

Step 1.1.2

Multiply $2$ by $2$ .

$2 y + 4 - 5 (y - 3) = 7 y + 19 - 10 y$

Step 1.1.3

Apply the distributive property.

$2 y + 4 - 5 y - 5 \cdot - 3 = 7 y + 19 - 10 y$

Step 1.1.4

Multiply $- 5$ by $- 3$ .

$2 y + 4 - 5 y + 15 = 7 y + 19 - 10 y$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $5 y$ from $2 y$ .

$- 3 y + 4 + 15 = 7 y + 19 - 10 y$

Step 1.2.2

Add $4$ and $15$ .

$- 3 y + 19 = 7 y + 19 - 10 y$

Step 2

Subtract $10 y$ from $7 y$ .

$- 3 y + 19 = - 3 y + 19$

Step 3

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

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Step 3.1

Add $3 y$ to both sides of the equation.

$- 3 y + 19 + 3 y = 19$

Step 3.2

Combine the opposite terms in $- 3 y + 19 + 3 y$ .

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Step 3.2.1

Add $- 3 y$ and $3 y$ .

$0 + 19 = 19$

Step 3.2.2

Add $0$ and $19$ .

$19 = 19$

Step 4

Since $19 = 19$ , the equation will always be true for any value of $y$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$