Algebra Examples

$7 t + 3 x = 4 t - 5 y$

Step 1

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

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Step 1.1

Subtract $4 t$ from both sides of the equation.

$7 t + 3 x - 4 t = - 5 y$

Step 1.2

Subtract $4 t$ from $7 t$ .

$3 t + 3 x = - 5 y$

Step 2

Subtract $3 x$ from both sides of the equation.

$3 t = - 5 y - 3 x$

Step 3

Divide each term in $3 t = - 5 y - 3 x$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 t = - 5 y - 3 x$ by $3$ .

$\frac{3 t}{3} = \frac{- 5 y}{3} + \frac{- 3 x}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 t}{3} = \frac{- 5 y}{3} + \frac{- 3 x}{3}$

Step 3.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 5 y}{3} + \frac{- 3 x}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$t = - \frac{5 y}{3} + \frac{- 3 x}{3}$

Step 3.3.1.2

Cancel the common factor of $- 3$ and $3$ .

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Step 3.3.1.2.1

Factor $3$ out of $- 3 x$ .

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

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $3$ out of $3$ .

$t = - \frac{5 y}{3} + \frac{3 (- x)}{3 (1)}$

Step 3.3.1.2.2.2

Cancel the common factor.

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

Step 3.3.1.2.2.3

Rewrite the expression.

$t = - \frac{5 y}{3} + \frac{- x}{1}$

Step 3.3.1.2.2.4

Divide $- x$ by $1$ .

$t = - \frac{5 y}{3} - x$