Finite Math Examples

$x + \frac{4 - z}{8} = 7$

Step 1

Simplify $x + \frac{4 - z}{8}$ .

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x \cdot \frac{8}{8} + \frac{4 - z}{8} = 7$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $x$ and $\frac{8}{8}$ .

$\frac{x \cdot 8}{8} + \frac{4 - z}{8} = 7$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x \cdot 8 + 4 - z}{8} = 7$

Step 1.3

Move $8$ to the left of $x$ .

$\frac{8 x + 4 - z}{8} = 7$

Step 2

Multiply both sides by $8$ .

$\frac{8 x + 4 - z}{8} \cdot 8 = 7 \cdot 8$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8 x + 4 - z}{8} \cdot 8$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{8 x + 4 - z}{8} \cdot 8 = 7 \cdot 8$

Step 3.1.1.1.2

Rewrite the expression.

$8 x + 4 - z = 7 \cdot 8$

Step 3.1.1.2

Move $4$ .

$8 x - z + 4 = 7 \cdot 8$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $7$ by $8$ .

$8 x - z + 4 = 56$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $z$ to both sides of the equation.

$8 x + 4 = 56 + z$

Step 4.1.2

Subtract $4$ from both sides of the equation.

$8 x = 56 + z - 4$

Step 4.1.3

Subtract $4$ from $56$ .

$8 x = z + 52$

Step 4.2

Divide each term in $8 x = z + 52$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = z + 52$ by $8$ .

$\frac{8 x}{8} = \frac{z}{8} + \frac{52}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{z}{8} + \frac{52}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{z}{8} + \frac{52}{8}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $52$ and $8$ .

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Step 4.2.3.1.1

Factor $4$ out of $52$ .

$x = \frac{z}{8} + \frac{4 (13)}{8}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $4$ out of $8$ .

$x = \frac{z}{8} + \frac{4 \cdot 13}{4 \cdot 2}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{z}{8} + \frac{4 \cdot 13}{4 \cdot 2}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{z}{8} + \frac{13}{2}$