Algebra Examples

$9 x - 7 i > 3 (3 x - 7 u)$

Step 1

Subtract $3 (3 x - 7 u)$ from both sides of the inequality.

$9 x - 7 i - 3 (3 x - 7 u) > 0$

Step 2

Simplify $9 x - 7 i - 3 (3 x - 7 u)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$9 x - 7 i - 3 (3 x) - 3 (- 7 u) > 0$

Step 2.1.2

Multiply $3$ by $- 3$ .

$9 x - 7 i - 9 x - 3 (- 7 u) > 0$

Step 2.1.3

Multiply $- 7$ by $- 3$ .

$9 x - 7 i - 9 x + 21 u > 0$

Step 2.2

Combine the opposite terms in $9 x - 7 i - 9 x + 21 u$ .

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Step 2.2.1

Subtract $9 x$ from $9 x$ .

$0 - 7 i + 21 u > 0$

Step 2.2.2

Subtract $7 i$ from $0$ .

$- 7 i + 21 u > 0$

Step 3

Factor $7$ out of $- 7 i + 21 u$ .

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Step 3.1

Factor $7$ out of $- 7 i$ .

$7 (- i) + 21 u > 0$

Step 3.2

Factor $7$ out of $21 u$ .

$7 (- i) + 7 (3 u) > 0$

Step 3.3

Factor $7$ out of $7 (- i) + 7 (3 u)$ .

$7 (- i + 3 u) > 0$

Step 4

Divide each term in $7 (- i + 3 u) > 0$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 (- i + 3 u) > 0$ by $7$ .

$\frac{7 (- i + 3 u)}{7} > \frac{0}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 (- i + 3 u)}{7} > \frac{0}{7}$

Step 4.2.1.2

Divide $- i + 3 u$ by $1$ .

$- i + 3 u > \frac{0}{7}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $7$ .

$- i + 3 u > 0$

Step 5

Add $i$ to both sides of the inequality.

$3 u > i$

Step 6

Divide each term in $3 u > i$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 u > i$ by $3$ .

$\frac{3 u}{3} > \frac{i}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 u}{3} > \frac{i}{3}$

Step 6.2.1.2

Divide $u$ by $1$ .

$u > \frac{i}{3}$