Pre-Algebra Examples

$3 (x + 1) - 7 = (\frac{1}{2}) x + 2 ((\frac{5}{4}) x - 2)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{1}{2} x + 2 (\frac{5}{4} x - 2) = 3 (x + 1) - 7$

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + 2 (\frac{5}{4} x - 2) = 3 (x + 1) - 7$

Step 2.1.2

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

$\frac{x}{2} + 2 (\frac{5 x}{4} - 2) = 3 (x + 1) - 7$

Step 2.1.3

Apply the distributive property.

$\frac{x}{2} + 2 \frac{5 x}{4} + 2 \cdot - 2 = 3 (x + 1) - 7$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Factor $2$ out of $4$ .

$\frac{x}{2} + 2 \frac{5 x}{2 (2)} + 2 \cdot - 2 = 3 (x + 1) - 7$

Step 2.1.4.2

Cancel the common factor.

$\frac{x}{2} + 2 \frac{5 x}{2 \cdot 2} + 2 \cdot - 2 = 3 (x + 1) - 7$

Step 2.1.4.3

Rewrite the expression.

$\frac{x}{2} + \frac{5 x}{2} + 2 \cdot - 2 = 3 (x + 1) - 7$

Step 2.1.5

Multiply $2$ by $- 2$ .

$\frac{x}{2} + \frac{5 x}{2} - 4 = 3 (x + 1) - 7$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$- 4 + \frac{x + 5 x}{2} = 3 (x + 1) - 7$

Step 2.2.2

Add $x$ and $5 x$ .

$- 4 + \frac{6 x}{2} = 3 (x + 1) - 7$

Step 2.2.3

Cancel the common factor of $6$ and $2$ .

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Step 2.2.3.1

Factor $2$ out of $6 x$ .

$- 4 + \frac{2 (3 x)}{2} = 3 (x + 1) - 7$

Step 2.2.3.2

Cancel the common factors.

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Step 2.2.3.2.1

Factor $2$ out of $2$ .

$- 4 + \frac{2 (3 x)}{2 (1)} = 3 (x + 1) - 7$

Step 2.2.3.2.2

Cancel the common factor.

$- 4 + \frac{2 (3 x)}{2 \cdot 1} = 3 (x + 1) - 7$

Step 2.2.3.2.3

Rewrite the expression.

$- 4 + \frac{3 x}{1} = 3 (x + 1) - 7$

Step 2.2.3.2.4

Divide $3 x$ by $1$ .

$- 4 + 3 x = 3 (x + 1) - 7$

Step 3

Simplify $3 (x + 1) - 7$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 4 + 3 x = 3 x + 3 \cdot 1 - 7$

Step 3.1.2

Multiply $3$ by $1$ .

$- 4 + 3 x = 3 x + 3 - 7$

Step 3.2

Subtract $7$ from $3$ .

$- 4 + 3 x = 3 x - 4$

Step 4

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

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Step 4.1

Subtract $3 x$ from both sides of the equation.

$- 4 + 3 x - 3 x = - 4$

Step 4.2

Combine the opposite terms in $- 4 + 3 x - 3 x$ .

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Step 4.2.1

Subtract $3 x$ from $3 x$ .

$- 4 + 0 = - 4$

Step 4.2.2

Add $- 4$ and $0$ .

$- 4 = - 4$

Step 5

Since $- 4 = - 4$ , the equation will always be true.

Always true