Algebra Examples

$\frac{7}{3} t - 5 = 19$

Step 1

Combine $\frac{7}{3}$ and $t$ .

$\frac{7 t}{3} - 5 = 19$

Step 2

Move all terms not containing $t$ to the right side of the equation.

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Step 2.1

Add $5$ to both sides of the equation.

$\frac{7 t}{3} = 19 + 5$

Step 2.2

Add $19$ and $5$ .

$\frac{7 t}{3} = 24$

Step 3

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} \cdot \frac{7 t}{3} = \frac{3}{7} \cdot 24$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{7} \cdot \frac{7 t}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 t}{3} = \frac{3}{7} \cdot 24$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 t) = \frac{3}{7} \cdot 24$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 t$ .

$\frac{1}{7} (7 (t)) = \frac{3}{7} \cdot 24$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 t) = \frac{3}{7} \cdot 24$

Step 4.1.1.2.3

Rewrite the expression.

$t = \frac{3}{7} \cdot 24$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{3}{7} \cdot 24$ .

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Step 4.2.1.1

Combine $\frac{3}{7}$ and $24$ .

$t = \frac{3 \cdot 24}{7}$

Step 4.2.1.2

Multiply $3$ by $24$ .

$t = \frac{72}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{72}{7}$

Decimal Form:

$t = 10.28571428 \dots$

Mixed Number Form:

$t = 10 \frac{2}{7}$