Finite Math Examples

$5 (x + 3) = 2 (x - 3) + 3 (x + 7)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 (x - 3) + 3 (x + 7) = 5 (x + 3)$

Step 2

Simplify $2 (x - 3) + 3 (x + 7)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x + 2 \cdot - 3 + 3 (x + 7) = 5 (x + 3)$

Step 2.1.2

Multiply $2$ by $- 3$ .

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

Step 2.1.3

Apply the distributive property.

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

Step 2.1.4

Multiply $3$ by $7$ .

$2 x - 6 + 3 x + 21 = 5 (x + 3)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $2 x$ and $3 x$ .

$5 x - 6 + 21 = 5 (x + 3)$

Step 2.2.2

Add $- 6$ and $21$ .

$5 x + 15 = 5 (x + 3)$

Step 3

Simplify $5 (x + 3)$ .

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Step 3.1

Apply the distributive property.

$5 x + 15 = 5 x + 5 \cdot 3$

Step 3.2

Multiply $5$ by $3$ .

$5 x + 15 = 5 x + 15$

Step 4

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

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Step 4.1

Subtract $5 x$ from both sides of the equation.

$5 x + 15 - 5 x = 15$

Step 4.2

Combine the opposite terms in $5 x + 15 - 5 x$ .

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Step 4.2.1

Subtract $5 x$ from $5 x$ .

$0 + 15 = 15$

Step 4.2.2

Add $0$ and $15$ .

$15 = 15$

Step 5

Since $15 = 15$ , the equation will always be true for any value of $x$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$