Algebra Examples

$2 (1 - \frac{5}{2} d) + 5 d = 2$

Step 1

Simplify $2 (1 - \frac{5}{2} d) + 5 d$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $d$ and $\frac{5}{2}$ .

$2 (1 - \frac{d \cdot 5}{2}) + 5 d = 2$

Step 1.1.1.2

Move $5$ to the left of $d$ .

$2 (1 - \frac{5 d}{2}) + 5 d = 2$

Step 1.1.2

Apply the distributive property.

$2 \cdot 1 + 2 (- \frac{5 d}{2}) + 5 d = 2$

Step 1.1.3

Multiply $2$ by $1$ .

$2 + 2 (- \frac{5 d}{2}) + 5 d = 2$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{5 d}{2}$ into the numerator.

$2 + 2 \frac{- 5 d}{2} + 5 d = 2$

Step 1.1.4.2

Cancel the common factor.

$2 + 2 \frac{- 5 d}{2} + 5 d = 2$

Step 1.1.4.3

Rewrite the expression.

$2 - 5 d + 5 d = 2$

Step 1.2

Combine the opposite terms in $2 - 5 d + 5 d$ .

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Step 1.2.1

Add $- 5 d$ and $5 d$ .

$2 + 0 = 2$

Step 1.2.2

Add $2$ and $0$ .

$2 = 2$

Step 2

Since $2 = 2$ , the equation will always be true for any value of $d$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$