Basic Math Examples

$3 (y + 3) + 5 y = 4 (2 y + 1) + 5$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 y + 3 \cdot 3 + 5 y = 4 (2 y + 1) + 5$

Step 1.1.2

Multiply $3$ by $3$ .

$3 y + 9 + 5 y = 4 (2 y + 1) + 5$

Step 1.2

Add $3 y$ and $5 y$ .

$8 y + 9 = 4 (2 y + 1) + 5$

Step 2

Simplify $4 (2 y + 1) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$8 y + 9 = 4 (2 y) + 4 \cdot 1 + 5$

Step 2.1.2

Multiply $2$ by $4$ .

$8 y + 9 = 8 y + 4 \cdot 1 + 5$

Step 2.1.3

Multiply $4$ by $1$ .

$8 y + 9 = 8 y + 4 + 5$

Step 2.2

Add $4$ and $5$ .

$8 y + 9 = 8 y + 9$

Step 3

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

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Step 3.1

Subtract $8 y$ from both sides of the equation.

$8 y + 9 - 8 y = 9$

Step 3.2

Combine the opposite terms in $8 y + 9 - 8 y$ .

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Step 3.2.1

Subtract $8 y$ from $8 y$ .

$0 + 9 = 9$

Step 3.2.2

Add $0$ and $9$ .

$9 = 9$

Step 4

Since $9 = 9$ , 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:

$(- \infty, \infty)$