Algebra Examples

$3 (1 - \frac{5}{2} x) + 4 x = 5$

Step 1

Simplify $3 (1 - \frac{5}{2} x) + 4 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $x$ and $\frac{5}{2}$ .

$3 (1 - \frac{x \cdot 5}{2}) + 4 x = 5$

Step 1.1.1.2

Move $5$ to the left of $x$ .

$3 (1 - \frac{5 x}{2}) + 4 x = 5$

Step 1.1.2

Apply the distributive property.

$3 \cdot 1 + 3 (- \frac{5 x}{2}) + 4 x = 5$

Step 1.1.3

Multiply $3$ by $1$ .

$3 + 3 (- \frac{5 x}{2}) + 4 x = 5$

Step 1.1.4

Multiply $3 (- \frac{5 x}{2})$ .

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Step 1.1.4.1

Multiply $- 1$ by $3$ .

$3 - 3 \frac{5 x}{2} + 4 x = 5$

Step 1.1.4.2

Combine $- 3$ and $\frac{5 x}{2}$ .

$3 + \frac{- 3 (5 x)}{2} + 4 x = 5$

Step 1.1.4.3

Multiply $5$ by $- 3$ .

$3 + \frac{- 15 x}{2} + 4 x = 5$

Step 1.1.5

Move the negative in front of the fraction.

$3 - \frac{15 x}{2} + 4 x = 5$

Step 1.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 - \frac{15 x}{2} + 4 x \cdot \frac{2}{2} = 5$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $4 x$ and $\frac{2}{2}$ .

$3 - \frac{15 x}{2} + \frac{4 x \cdot 2}{2} = 5$

Step 1.3.2

Combine the numerators over the common denominator.

$3 + \frac{- 15 x + 4 x \cdot 2}{2} = 5$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $x$ out of $- 15 x + 4 x \cdot 2$ .

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Step 1.4.1.1.1

Factor $x$ out of $- 15 x$ .

$3 + \frac{x \cdot - 15 + 4 x \cdot 2}{2} = 5$

Step 1.4.1.1.2

Factor $x$ out of $4 x \cdot 2$ .

$3 + \frac{x \cdot - 15 + x (4 \cdot 2)}{2} = 5$

Step 1.4.1.1.3

Factor $x$ out of $x \cdot - 15 + x (4 \cdot 2)$ .

$3 + \frac{x (- 15 + 4 \cdot 2)}{2} = 5$

Step 1.4.1.2

Multiply $4$ by $2$ .

$3 + \frac{x (- 15 + 8)}{2} = 5$

Step 1.4.1.3

Add $- 15$ and $8$ .

$3 + \frac{x \cdot - 7}{2} = 5$

Step 1.4.2

Move $- 7$ to the left of $x$ .

$3 + \frac{- 7 \cdot x}{2} = 5$

Step 1.4.3

Move the negative in front of the fraction.

$3 - \frac{7 x}{2} = 5$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the equation.

$- \frac{7 x}{2} = 5 - 3$

Step 2.2

Subtract $3$ from $5$ .

$- \frac{7 x}{2} = 2$

Step 3

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot 2$

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 $- \frac{2}{7} (- \frac{7 x}{2})$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot 2$

Step 4.1.1.1.2

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot 2$

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot 2$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot 2$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{2}{7} \cdot 2$

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 $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot 2$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot 2$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{2}{7} \cdot 2$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{7} \cdot 2$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{2}{7} \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{2}{7} \cdot 2$ .

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Step 4.2.1.1

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

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Step 4.2.1.1.1

Multiply $2$ by $- 1$ .

$x = - 2 (\frac{2}{7})$

Step 4.2.1.1.2

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

$x = \frac{- 2 \cdot 2}{7}$

Step 4.2.1.1.3

Multiply $- 2$ by $2$ .

$x = \frac{- 4}{7}$

Step 4.2.1.2

Move the negative in front of the fraction.

$x = - \frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{7}$

Decimal Form:

$x = - 0.\overline{571428}$