Algebra Examples

$\frac{1}{2} (x + 2) + 3 y < 8$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} x + \frac{1}{2} \cdot 2 + 3 y < 8$

Step 1.2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{1}{2} \cdot 2 + 3 y < 8$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$\frac{x}{2} + \frac{1}{2} \cdot 2 + 3 y < 8$

Step 1.3.2

Rewrite the expression.

$\frac{x}{2} + 1 + 3 y < 8$

$\frac{x}{2} + 1 + 3 y < 8$

$\frac{x}{2} + 1 + 3 y < 8$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1

Subtract $1$ from both sides of the inequality.

$\frac{x}{2} + 3 y < 8 - 1$

Step 2.2

Subtract $3 y$ from both sides of the inequality.

$\frac{x}{2} < 8 - 1 - 3 y$

Step 2.3

Subtract $1$ from $8$ .

$\frac{x}{2} < 7 - 3 y$

$\frac{x}{2} < 7 - 3 y$

Step 3

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 < (7 - 3 y) \cdot 2$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{x}{2} \cdot 2 < (7 - 3 y) \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$x < (7 - 3 y) \cdot 2$

$x < (7 - 3 y) \cdot 2$

$x < (7 - 3 y) \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $(7 - 3 y) \cdot 2$ .

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Step 4.2.1.1

Apply the distributive property.

$x < 7 \cdot 2 - 3 y \cdot 2$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $7$ by $2$ .

$x < 14 - 3 y \cdot 2$

Step 4.2.1.2.2

Multiply $2$ by $- 3$ .

$x < 14 - 6 y$

Step 4.2.1.2.3

Reorder $14$ and $- 6 y$ .

$x < - 6 y + 14$

$x < - 6 y + 14$

$x < - 6 y + 14$

$x < - 6 y + 14$

$x < - 6 y + 14$

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