Pre-Algebra Examples

$6 (x - 2) + 1 = 2 (3 x - 5)$

Step 1

Simplify $6 (x - 2) + 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 x + 6 \cdot - 2 + 1 = 2 (3 x - 5)$

Step 1.1.2

Multiply $6$ by $- 2$ .

$6 x - 12 + 1 = 2 (3 x - 5)$

$6 x - 12 + 1 = 2 (3 x - 5)$

Step 1.2

Add $- 12$ and $1$ .

$6 x - 11 = 2 (3 x - 5)$

$6 x - 11 = 2 (3 x - 5)$

Step 2

Simplify $2 (3 x - 5)$ .

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Step 2.1

Apply the distributive property.

$6 x - 11 = 2 (3 x) + 2 \cdot - 5$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $2$ .

$6 x - 11 = 6 x + 2 \cdot - 5$

Step 2.2.2

Multiply $2$ by $- 5$ .

$6 x - 11 = 6 x - 10$

$6 x - 11 = 6 x - 10$

$6 x - 11 = 6 x - 10$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the equation.

$6 x - 11 - 6 x = - 10$

Step 3.2

Combine the opposite terms in $6 x - 11 - 6 x$ .

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Step 3.2.1

Subtract $6 x$ from $6 x$ .

$0 - 11 = - 10$

Step 3.2.2

Subtract $11$ from $0$ .

$- 11 = - 10$

$- 11 = - 10$

$- 11 = - 10$

Step 4

Since $- 11 \neq - 10$ , there are no solutions.

No solution

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$