Algebra Examples

$\frac{5}{3} z + 1 = 3 - \frac{2}{3} z$

Step 1

Combine $\frac{5}{3}$ and $z$ .

$\frac{5 z}{3} + 1 = 3 - \frac{2}{3} z$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{5 z}{3} + 1 = 3 - \frac{z \cdot 2}{3}$

Step 2.2

Move $2$ to the left of $z$ .

$\frac{5 z}{3} + 1 = 3 - \frac{2 z}{3}$

Step 3

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

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Step 3.1

Add $\frac{2 z}{3}$ to both sides of the equation.

$\frac{5 z}{3} + 1 + \frac{2 z}{3} = 3$

Step 3.2

Combine the numerators over the common denominator.

$1 + \frac{5 z + 2 z}{3} = 3$

Step 3.3

Add $5 z$ and $2 z$ .

$1 + \frac{7 z}{3} = 3$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$\frac{7 z}{3} = 3 - 1$

Step 4.2

Subtract $1$ from $3$ .

$\frac{7 z}{3} = 2$

Step 5

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

$\frac{3}{7} \cdot \frac{7 z}{3} = \frac{3}{7} \cdot 2$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 z}{3} = \frac{3}{7} \cdot 2$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{3}{7} \cdot 2$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{3}{7} \cdot 2$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{3}{7} \cdot 2$

Step 6.1.1.2.3

Rewrite the expression.

$z = \frac{3}{7} \cdot 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{3}{7} \cdot 2$ .

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Step 6.2.1.1

Combine $\frac{3}{7}$ and $2$ .

$z = \frac{3 \cdot 2}{7}$

Step 6.2.1.2

Multiply $3$ by $2$ .

$z = \frac{6}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$z = \frac{6}{7}$

Decimal Form:

$z = 0.\overline{857142}$