Finite Math Examples

$4 x - 10 = 7$ , $8 x - 20 = 14$

Step 1

Solve for $x$ in $4 x - 10 = 7$ .

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Step 1.1

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

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Step 1.1.1

Add $10$ to both sides of the equation.

$4 x = 7 + 10$

$8 x - 20 = 14$

Step 1.1.2

Add $7$ and $10$ .

$4 x = 17$

$8 x - 20 = 14$

$4 x = 17$

$8 x - 20 = 14$

Step 1.2

Divide each term in $4 x = 17$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x = 17$ by $4$ .

$\frac{4 x}{4} = \frac{17}{4}$

$8 x - 20 = 14$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{17}{4}$

$8 x - 20 = 14$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{4}$

$8 x - 20 = 14$

$x = \frac{17}{4}$

$8 x - 20 = 14$

$x = \frac{17}{4}$

$8 x - 20 = 14$

$x = \frac{17}{4}$

$8 x - 20 = 14$

$x = \frac{17}{4}$

$8 x - 20 = 14$

Step 2

Replace all occurrences of $x$ with $\frac{17}{4}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $8 x - 20 = 14$ with $\frac{17}{4}$ .

$8 (\frac{17}{4}) - 20 = 14$

$x = \frac{17}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $8 (\frac{17}{4}) - 20$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1.1

Factor $4$ out of $8$ .

$4 (2) (\frac{17}{4}) - 20 = 14$

$x = \frac{17}{4}$

Step 2.2.1.1.1.2

Cancel the common factor.

$4 \cdot (2 (\frac{17}{4})) - 20 = 14$

$x = \frac{17}{4}$

Step 2.2.1.1.1.3

Rewrite the expression.

$2 \cdot 17 - 20 = 14$

$x = \frac{17}{4}$

$2 \cdot 17 - 20 = 14$

$x = \frac{17}{4}$

Step 2.2.1.1.2

Multiply $2$ by $17$ .

$34 - 20 = 14$

$x = \frac{17}{4}$

$34 - 20 = 14$

$x = \frac{17}{4}$

Step 2.2.1.2

Subtract $20$ from $34$ .

$14 = 14$

$x = \frac{17}{4}$

$14 = 14$

$x = \frac{17}{4}$

$14 = 14$

$x = \frac{17}{4}$

$14 = 14$

$x = \frac{17}{4}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{17}{4}$

Step 4