Finite Math Examples

$10 x + 6 = 8 (\frac{5}{4} x + \frac{3}{4})$

Step 1

Simplify $8 (\frac{5}{4} x + \frac{3}{4})$ .

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Step 1.1

Rewrite.

$10 x + 6 = 0 + 0 + 8 (\frac{5}{4} x + \frac{3}{4})$

Step 1.2

Simplify by adding zeros.

$10 x + 6 = 8 (\frac{5}{4} x + \frac{3}{4})$

Step 1.3

Combine $\frac{5}{4}$ and $x$ .

$10 x + 6 = 8 (\frac{5 x}{4} + \frac{3}{4})$

Step 1.4

Apply the distributive property.

$10 x + 6 = 8 \frac{5 x}{4} + 8 (\frac{3}{4})$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Factor $4$ out of $8$ .

$10 x + 6 = 4 (2) \frac{5 x}{4} + 8 (\frac{3}{4})$

Step 1.5.2

Cancel the common factor.

$10 x + 6 = 4 \cdot 2 \frac{5 x}{4} + 8 (\frac{3}{4})$

Step 1.5.3

Rewrite the expression.

$10 x + 6 = 2 (5 x) + 8 (\frac{3}{4})$

Step 1.6

Multiply $5$ by $2$ .

$10 x + 6 = 10 x + 8 (\frac{3}{4})$

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Factor $4$ out of $8$ .

$10 x + 6 = 10 x + 4 (2) \frac{3}{4}$

Step 1.7.2

Cancel the common factor.

$10 x + 6 = 10 x + 4 \cdot 2 \frac{3}{4}$

Step 1.7.3

Rewrite the expression.

$10 x + 6 = 10 x + 2 \cdot 3$

Step 1.8

Multiply $2$ by $3$ .

$10 x + 6 = 10 x + 6$

Step 2

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

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Step 2.1

Subtract $10 x$ from both sides of the equation.

$10 x + 6 - 10 x = 6$

Step 2.2

Combine the opposite terms in $10 x + 6 - 10 x$ .

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Step 2.2.1

Subtract $10 x$ from $10 x$ .

$0 + 6 = 6$

Step 2.2.2

Add $0$ and $6$ .

$6 = 6$

Step 3

Since $6 = 6$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$