Algebra Examples

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

Step 1

Simplify $4 x - \frac{1}{2} x - 7$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Simplify terms.

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Step 1.3.1

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

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

Step 1.3.2

Combine the numerators over the common denominator.

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

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 $4 x \cdot 2 - x$ .

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Step 1.4.1.1.1

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

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

Step 1.4.1.1.2

Factor $x$ out of $- x$ .

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

Step 1.4.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 1$ .

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

Step 1.4.1.2

Multiply $4$ by $2$ .

$\frac{x (8 - 1)}{2} - 7 = 7 (\frac{1}{2} x - 7)$

Step 1.4.1.3

Subtract $1$ from $8$ .

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

Step 1.4.2

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

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

Step 2

Simplify $7 (\frac{1}{2} x - 7)$ .

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Step 2.1

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

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

Step 2.2

Apply the distributive property.

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

Step 2.3

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

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

Step 2.4

Multiply $7$ by $- 7$ .

$\frac{7 x}{2} - 7 = \frac{7 x}{2} - 49$

Step 3

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

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Step 3.1

Subtract $\frac{7 x}{2}$ from both sides of the equation.

$\frac{7 x}{2} - 7 - \frac{7 x}{2} = - 49$

Step 3.2

Combine the opposite terms in $\frac{7 x}{2} - 7 - \frac{7 x}{2}$ .

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Step 3.2.1

Subtract $\frac{7 x}{2}$ from $\frac{7 x}{2}$ .

$0 - 7 = - 49$

Step 3.2.2

Subtract $7$ from $0$ .

$- 7 = - 49$

Step 4

Since $- 7 \neq - 49$ , there are no solutions.

No solution