Finite Math Examples

$\frac{5}{2} t - t = 3 + \frac{3}{2} t$

Step 1

Simplify $\frac{5}{2} t - t$ .

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Step 1.1

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

$\frac{5 t}{2} - t = 3 + \frac{3}{2} t$

Step 1.2

To write $- t$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 t}{2} - t \cdot \frac{2}{2} = 3 + \frac{3}{2} t$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- t$ and $\frac{2}{2}$ .

$\frac{5 t}{2} + \frac{- t \cdot 2}{2} = 3 + \frac{3}{2} t$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{5 t - t \cdot 2}{2} = 3 + \frac{3}{2} t$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $t$ out of $5 t - t \cdot 2$ .

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Step 1.4.1.1

Factor $t$ out of $5 t$ .

$\frac{t \cdot 5 - t \cdot 2}{2} = 3 + \frac{3}{2} t$

Step 1.4.1.2

Factor $t$ out of $- t \cdot 2$ .

$\frac{t \cdot 5 + t (- 1 \cdot 2)}{2} = 3 + \frac{3}{2} t$

Step 1.4.1.3

Factor $t$ out of $t \cdot 5 + t (- 1 \cdot 2)$ .

$\frac{t (5 - 1 \cdot 2)}{2} = 3 + \frac{3}{2} t$

Step 1.4.2

Multiply $- 1$ by $2$ .

$\frac{t (5 - 2)}{2} = 3 + \frac{3}{2} t$

Step 1.4.3

Subtract $2$ from $5$ .

$\frac{t \cdot 3}{2} = 3 + \frac{3}{2} t$

Step 1.5

Move $3$ to the left of $t$ .

$\frac{3 t}{2} = 3 + \frac{3}{2} t$

Step 2

Combine $\frac{3}{2}$ and $t$ .

$\frac{3 t}{2} = 3 + \frac{3 t}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{3 t}{2}$ from both sides of the equation.

$\frac{3 t}{2} - \frac{3 t}{2} = 3$

Step 3.2

Subtract $\frac{3 t}{2}$ from $\frac{3 t}{2}$ .

$0 = 3$

Step 4

Since $0 \neq 3$ , there are no solutions.

No solution