Algebra Examples

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

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

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

Step 1.2

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

$\frac{5}{2} t - t - 3 - \frac{3}{2} t = 0$

Step 2

Simplify $\frac{5}{2} t - t - 3 - \frac{3}{2} t$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{5 t}{2} - t - 3 - \frac{3}{2} t = 0$

Step 2.1.2

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

$\frac{5 t}{2} - t - 3 - \frac{t \cdot 3}{2} = 0$

Step 2.1.3

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

$\frac{5 t}{2} - t - 3 - \frac{3 t}{2} = 0$

Step 2.2

Combine the numerators over the common denominator.

$- t - 3 + \frac{5 t - 3 t}{2} = 0$

Step 2.3

Subtract $3 t$ from $5 t$ .

$- t - 3 + \frac{2 t}{2} = 0$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$- t - 3 + \frac{2 t}{2} = 0$

Step 2.4.2

Divide $t$ by $1$ .

$- t - 3 + t = 0$

Step 2.5

Combine the opposite terms in $- t - 3 + t$ .

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Step 2.5.1

Add $- t$ and $t$ .

$0 - 3 = 0$

Step 2.5.2

Subtract $3$ from $0$ .

$- 3 = 0$

Step 3

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

No solution