Pre-Algebra Examples

$0.02 (2 x - 5) = 0.04 (x + 7) - 0.38$

Step 1

Simplify $0.02 (2 x - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + 0.02 (2 x - 5) = 0.04 (x + 7) - 0.38$

Step 1.2

Simplify by adding zeros.

$0.02 (2 x - 5) = 0.04 (x + 7) - 0.38$

Step 1.3

Apply the distributive property.

$0.02 (2 x) + 0.02 \cdot - 5 = 0.04 (x + 7) - 0.38$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $0.02$ .

$0.04 x + 0.02 \cdot - 5 = 0.04 (x + 7) - 0.38$

Step 1.4.2

Multiply $0.02$ by $- 5$ .

$0.04 x - 0.1 = 0.04 (x + 7) - 0.38$

Step 2

Simplify $0.04 (x + 7) - 0.38$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$0.04 x - 0.1 = 0.04 x + 0.04 \cdot 7 - 0.38$

Step 2.1.2

Multiply $0.04$ by $7$ .

$0.04 x - 0.1 = 0.04 x + 0.28 - 0.38$

Step 2.2

Subtract $0.38$ from $0.28$ .

$0.04 x - 0.1 = 0.04 x - 0.1$

Step 3

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

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Step 3.1

Subtract $0.04 x$ from both sides of the equation.

$0.04 x - 0.1 - 0.04 x = - 0.1$

Step 3.2

Subtract $0.04 x$ from $0.04 x$ .

$0 x - 0.1 = - 0.1$

Step 3.3

Multiply $0$ by $x$ .

$0 - 0.1 = - 0.1$

Step 3.4

Subtract $0.1$ from $0$ .

$- 0.1 = - 0.1$

Step 4

Since $- 0.1 = - 0.1$ , 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:

$(- \infty, \infty)$