Pre-Algebra Examples

$8 - 3 (x - 5) + 7 = 3 - (x - 5) - 2 (x - 11)$

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.

$3 - (x - 5) - 2 (x - 11) = 8 - 3 (x - 5) + 7$

Step 2

Simplify $3 - (x - 5) - 2 (x - 11)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 - x - - 5 - 2 (x - 11) = 8 - 3 (x - 5) + 7$

Step 2.1.2

Multiply $- 1$ by $- 5$ .

$3 - x + 5 - 2 (x - 11) = 8 - 3 (x - 5) + 7$

Step 2.1.3

Apply the distributive property.

$3 - x + 5 - 2 x - 2 \cdot - 11 = 8 - 3 (x - 5) + 7$

Step 2.1.4

Multiply $- 2$ by $- 11$ .

$3 - x + 5 - 2 x + 22 = 8 - 3 (x - 5) + 7$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $3$ and $5$ .

$- x + 8 - 2 x + 22 = 8 - 3 (x - 5) + 7$

Step 2.2.2

Subtract $2 x$ from $- x$ .

$- 3 x + 8 + 22 = 8 - 3 (x - 5) + 7$

Step 2.2.3

Add $8$ and $22$ .

$- 3 x + 30 = 8 - 3 (x - 5) + 7$

Step 3

Simplify $8 - 3 (x - 5) + 7$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 3 x + 30 = 8 - 3 x - 3 \cdot - 5 + 7$

Step 3.1.2

Multiply $- 3$ by $- 5$ .

$- 3 x + 30 = 8 - 3 x + 15 + 7$

Step 3.2

Simplify by adding numbers.

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Step 3.2.1

Add $8$ and $15$ .

$- 3 x + 30 = - 3 x + 23 + 7$

Step 3.2.2

Add $23$ and $7$ .

$- 3 x + 30 = - 3 x + 30$

Step 4

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

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Step 4.1

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

$- 3 x + 30 + 3 x = 30$

Step 4.2

Combine the opposite terms in $- 3 x + 30 + 3 x$ .

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Step 4.2.1

Add $- 3 x$ and $3 x$ .

$0 + 30 = 30$

Step 4.2.2

Add $0$ and $30$ .

$30 = 30$

Step 5

Since $30 = 30$ , 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:

$(- \infty, \infty)$