Algebra Examples

$4 (x - 2) + x = \frac{1}{2} (10 x - 6)$

Step 1

Simplify $4 (x - 2) + x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 x + 4 \cdot - 2 + x = \frac{1}{2} \cdot (10 x - 6)$

Step 1.1.2

Multiply $4$ by $- 2$ .

$4 x - 8 + x = \frac{1}{2} \cdot (10 x - 6)$

Step 1.2

Add $4 x$ and $x$ .

$5 x - 8 = \frac{1}{2} \cdot (10 x - 6)$

Step 2

Simplify $\frac{1}{2} \cdot (10 x - 6)$ .

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Step 2.1

Apply the distributive property.

$5 x - 8 = \frac{1}{2} (10 x) + \frac{1}{2} \cdot - 6$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $10 x$ .

$5 x - 8 = \frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 6$

Step 2.2.2

Cancel the common factor.

$5 x - 8 = \frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 6$

Step 2.2.3

Rewrite the expression.

$5 x - 8 = 5 x + \frac{1}{2} \cdot - 6$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $- 6$ .

$5 x - 8 = 5 x + \frac{1}{2} \cdot (2 (- 3))$

Step 2.3.2

Cancel the common factor.

$5 x - 8 = 5 x + \frac{1}{2} \cdot (2 \cdot - 3)$

Step 2.3.3

Rewrite the expression.

$5 x - 8 = 5 x - 3$

Step 3

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

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Step 3.1

Subtract $5 x$ from both sides of the equation.

$5 x - 8 - 5 x = - 3$

Step 3.2

Combine the opposite terms in $5 x - 8 - 5 x$ .

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Step 3.2.1

Subtract $5 x$ from $5 x$ .

$0 - 8 = - 3$

Step 3.2.2

Subtract $8$ from $0$ .

$- 8 = - 3$

Step 4

Since $- 8 \neq - 3$ , there are no solutions.

No solution