Algebra Examples

$2 (x - 3) - 7 (5 - x) = 9 x - 45$

Step 1

Simplify $2 (x - 3) - 7 (5 - x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x + 2 \cdot - 3 - 7 (5 - x) = 9 x - 45$

Step 1.1.2

Multiply $2$ by $- 3$ .

$2 x - 6 - 7 (5 - x) = 9 x - 45$

Step 1.1.3

Apply the distributive property.

$2 x - 6 - 7 \cdot 5 - 7 (- x) = 9 x - 45$

Step 1.1.4

Multiply $- 7$ by $5$ .

$2 x - 6 - 35 - 7 (- x) = 9 x - 45$

Step 1.1.5

Multiply $- 1$ by $- 7$ .

$2 x - 6 - 35 + 7 x = 9 x - 45$

$2 x - 6 - 35 + 7 x = 9 x - 45$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $2 x$ and $7 x$ .

$9 x - 6 - 35 = 9 x - 45$

Step 1.2.2

Subtract $35$ from $- 6$ .

$9 x - 41 = 9 x - 45$

$9 x - 41 = 9 x - 45$

$9 x - 41 = 9 x - 45$

Step 2

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

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Step 2.1

Subtract $9 x$ from both sides of the equation.

$9 x - 41 - 9 x = - 45$

Step 2.2

Combine the opposite terms in $9 x - 41 - 9 x$ .

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Step 2.2.1

Subtract $9 x$ from $9 x$ .

$0 - 41 = - 45$

Step 2.2.2

Subtract $41$ from $0$ .

$- 41 = - 45$

$- 41 = - 45$

$- 41 = - 45$

Step 3

Since $- 41 \neq - 45$ , there are no solutions.

No solution

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