Algebra Examples

$6 a + 4 b \geq 10$

Step 1

Subtract $4 b$ from both sides of the inequality.

$6 a \geq 10 - 4 b$

Step 2

Divide each term in $6 a \geq 10 - 4 b$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 a \geq 10 - 4 b$ by $6$ .

$\frac{6 a}{6} \geq \frac{10}{6} + \frac{- 4 b}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 a}{6} \geq \frac{10}{6} + \frac{- 4 b}{6}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a \geq \frac{10}{6} + \frac{- 4 b}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $10$ and $6$ .

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Step 2.3.1.1.1

Factor $2$ out of $10$ .

$a \geq \frac{2 (5)}{6} + \frac{- 4 b}{6}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $6$ .

$a \geq \frac{2 \cdot 5}{2 \cdot 3} + \frac{- 4 b}{6}$

Step 2.3.1.1.2.2

Cancel the common factor.

$a \geq \frac{2 \cdot 5}{2 \cdot 3} + \frac{- 4 b}{6}$

Step 2.3.1.1.2.3

Rewrite the expression.

$a \geq \frac{5}{3} + \frac{- 4 b}{6}$

Step 2.3.1.2

Cancel the common factor of $- 4$ and $6$ .

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Step 2.3.1.2.1

Factor $2$ out of $- 4 b$ .

$a \geq \frac{5}{3} + \frac{2 (- 2 b)}{6}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $6$ .

$a \geq \frac{5}{3} + \frac{2 (- 2 b)}{2 (3)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$a \geq \frac{5}{3} + \frac{2 (- 2 b)}{2 \cdot 3}$

Step 2.3.1.2.2.3

Rewrite the expression.

$a \geq \frac{5}{3} + \frac{- 2 b}{3}$

Step 2.3.1.3

Move the negative in front of the fraction.

$a \geq \frac{5}{3} - \frac{2 b}{3}$