Pre-Algebra Examples

$5 (u + 1) - 7 = 3 (u - 1) + 2 u$

Step 1

Since $u$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 (u - 1) + 2 u = 5 (u + 1) - 7$

Step 2

Simplify $3 (u - 1) + 2 u$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 u + 3 \cdot - 1 + 2 u = 5 (u + 1) - 7$

Step 2.1.2

Multiply $3$ by $- 1$ .

$3 u - 3 + 2 u = 5 (u + 1) - 7$

Step 2.2

Add $3 u$ and $2 u$ .

$5 u - 3 = 5 (u + 1) - 7$

Step 3

Simplify $5 (u + 1) - 7$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$5 u - 3 = 5 u + 5 \cdot 1 - 7$

Step 3.1.2

Multiply $5$ by $1$ .

$5 u - 3 = 5 u + 5 - 7$

Step 3.2

Subtract $7$ from $5$ .

$5 u - 3 = 5 u - 2$

Step 4

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

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Step 4.1

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

$5 u - 3 - 5 u = - 2$

Step 4.2

Combine the opposite terms in $5 u - 3 - 5 u$ .

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Step 4.2.1

Subtract $5 u$ from $5 u$ .

$0 - 3 = - 2$

Step 4.2.2

Subtract $3$ from $0$ .

$- 3 = - 2$

Step 5

Since $- 3 \neq - 2$ , there are no solutions.

No solution