Solve for x 4(2.5x-2)=2(5x-5)+2

$4 (2.5 x - 2) = 2 (5 x - 5) + 2$

Simplify $4 (2.5 x - 2)$ .

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Apply the distributive property.

$4 (2.5 x) + 4 \cdot - 2 = 2 (5 x - 5) + 2$

Multiply.

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Multiply $2.5$ by $4$ .

$10 x + 4 \cdot - 2 = 2 (5 x - 5) + 2$

Multiply $4$ by $- 2$ .

$10 x - 8 = 2 (5 x - 5) + 2$

Simplify $2 (5 x - 5) + 2$ .

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Simplify each term.

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Apply the distributive property.

$10 x - 8 = 2 (5 x) + 2 \cdot - 5 + 2$

Multiply $5$ by $2$ .

$10 x - 8 = 10 x + 2 \cdot - 5 + 2$

Multiply $2$ by $- 5$ .

$10 x - 8 = 10 x - 10 + 2$

Add $- 10$ and $2$ .

$10 x - 8 = 10 x - 8$

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

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Subtract $10 x$ from both sides of the equation.

$10 x - 8 - 10 x = - 8$

Subtract $10 x$ from $10 x$ .

$0 x - 8 = - 8$

Multiply $0$ by $x$ .

$0 - 8 = - 8$

Subtract $8$ from $0$ .

$- 8 = - 8$

Since $- 8 = - 8$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve for x 4(2.5x-2)=2(5x-5)+2

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