Algebra Examples

3 d + 4 = 2 + 3 d - \frac{1}{2}

$3 d + 4 = 2 + 3 d - \frac{1}{2}$

Step 1

Simplify

2 + 3 d - \frac{1}{2}

$2 + 3 d - \frac{1}{2}$ .

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Step 1.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

3 d + 4 = 3 d + 2 \cdot \frac{2}{2} - \frac{1}{2}

$3 d + 4 = 3 d + 2 \cdot \frac{2}{2} - \frac{1}{2}$

Step 1.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

3 d + 4 = 3 d + \frac{2 \cdot 2}{2} - \frac{1}{2}

$3 d + 4 = 3 d + \frac{2 \cdot 2}{2} - \frac{1}{2}$

Step 1.3

Combine the numerators over the common denominator.

3 d + 4 = 3 d + \frac{2 \cdot 2 - 1}{2}

$3 d + 4 = 3 d + \frac{2 \cdot 2 - 1}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply

2

$2$ by

2

$2$ .

3 d + 4 = 3 d + \frac{4 - 1}{2}

$3 d + 4 = 3 d + \frac{4 - 1}{2}$

Step 1.4.2

Subtract

1

$1$ from

4

$4$ .

3 d + 4 = 3 d + \frac{3}{2}

$3 d + 4 = 3 d + \frac{3}{2}$

3 d + 4 = 3 d + \frac{3}{2}

$3 d + 4 = 3 d + \frac{3}{2}$

3 d + 4 = 3 d + \frac{3}{2}

$3 d + 4 = 3 d + \frac{3}{2}$

Step 2

Move all terms containing

d

$d$ to the left side of the equation.

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Step 2.1

Subtract

3 d

$3 d$ from both sides of the equation.

3 d + 4 - 3 d = \frac{3}{2}

$3 d + 4 - 3 d = \frac{3}{2}$

Step 2.2

Combine the opposite terms in

3 d + 4 - 3 d

$3 d + 4 - 3 d$ .

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Step 2.2.1

Subtract

3 d

$3 d$ from

3 d

$3 d$ .

0 + 4 = \frac{3}{2}

$0 + 4 = \frac{3}{2}$

Step 2.2.2

Add

0

$0$ and

4

$4$ .

4 = \frac{3}{2}

$4 = \frac{3}{2}$

4 = \frac{3}{2}

$4 = \frac{3}{2}$

4 = \frac{3}{2}

$4 = \frac{3}{2}$

Step 3

Since

4 \neq \frac{3}{2}

$4 \neq \frac{3}{2}$ , there are no solutions.

No solution