Algebra Examples

$3 - 3 (1 + \frac{4}{3} t) = 2 + 6 (3 - \frac{5}{6} t)$

Step 1

Simplify $3 - 3 (1 + \frac{4}{3} t)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{4}{3}$ and $t$ .

$3 - 3 (1 + \frac{4 t}{3}) = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.2

Apply the distributive property.

$3 - 3 \cdot 1 - 3 \frac{4 t}{3} = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.3

Multiply $- 3$ by $1$ .

$3 - 3 - 3 \frac{4 t}{3} = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Factor $3$ out of $- 3$ .

$3 - 3 + 3 (- 1) \frac{4 t}{3} = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.4.2

Cancel the common factor.

$3 - 3 + 3 \cdot - 1 \frac{4 t}{3} = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.4.3

Rewrite the expression.

$3 - 3 - 1 (4 t) = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.1.5

Multiply $4$ by $- 1$ .

$3 - 3 - 4 t = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.2

Simplify by subtracting numbers.

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Step 1.2.1

Subtract $3$ from $3$ .

$0 - 4 t = 2 + 6 (3 - \frac{5}{6} t)$

Step 1.2.2

Subtract $4 t$ from $0$ .

$- 4 t = 2 + 6 (3 - \frac{5}{6} t)$

Step 2

Simplify $2 + 6 (3 - \frac{5}{6} t)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $t$ and $\frac{5}{6}$ .

$- 4 t = 2 + 6 (3 - \frac{t \cdot 5}{6})$

Step 2.1.1.2

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

$- 4 t = 2 + 6 (3 - \frac{5 t}{6})$

Step 2.1.2

Apply the distributive property.

$- 4 t = 2 + 6 \cdot 3 + 6 (- \frac{5 t}{6})$

Step 2.1.3

Multiply $6$ by $3$ .

$- 4 t = 2 + 18 + 6 (- \frac{5 t}{6})$

Step 2.1.4

Cancel the common factor of $6$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{5 t}{6}$ into the numerator.

$- 4 t = 2 + 18 + 6 \frac{- 5 t}{6}$

Step 2.1.4.2

Cancel the common factor.

$- 4 t = 2 + 18 + 6 \frac{- 5 t}{6}$

Step 2.1.4.3

Rewrite the expression.

$- 4 t = 2 + 18 - 5 t$

Step 2.2

Add $2$ and $18$ .

$- 4 t = 20 - 5 t$

Step 3

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

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Step 3.1

Add $5 t$ to both sides of the equation.

$- 4 t + 5 t = 20$

Step 3.2

Add $- 4 t$ and $5 t$ .

$t = 20$