Pre-Algebra Examples

$4 (2.5 x - 2) = 2 (5 x - 5) + 2$

Step 1

Simplify $4 (2.5 x - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 (2.5 x - 2) = 2 (5 x - 5) + 2$

Step 1.2

Simplify by adding zeros.

$4 (2.5 x - 2) = 2 (5 x - 5) + 2$

Step 1.3

Apply the distributive property.

$4 (2.5 x) + 4 \cdot - 2 = 2 (5 x - 5) + 2$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2.5$ by $4$ .

$10 x + 4 \cdot - 2 = 2 (5 x - 5) + 2$

Step 1.4.2

Multiply $4$ by $- 2$ .

$10 x - 8 = 2 (5 x - 5) + 2$

Step 2

Simplify $2 (5 x - 5) + 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$10 x - 8 = 2 (5 x) + 2 \cdot - 5 + 2$

Step 2.1.2

Multiply $5$ by $2$ .

$10 x - 8 = 10 x + 2 \cdot - 5 + 2$

Step 2.1.3

Multiply $2$ by $- 5$ .

$10 x - 8 = 10 x - 10 + 2$

Step 2.2

Add $- 10$ and $2$ .

$10 x - 8 = 10 x - 8$

Step 3

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

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Step 3.1

Subtract $10 x$ from both sides of the equation.

$10 x - 8 - 10 x = - 8$

Step 3.2

Subtract $10 x$ from $10 x$ .

$0 x - 8 = - 8$

Step 3.3

Multiply $0$ by $x$ .

$0 - 8 = - 8$

Step 3.4

Subtract $8$ from $0$ .

$- 8 = - 8$

Step 4

Since $- 8 = - 8$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$