Algebra Examples

$y \leq \frac{5}{3} x - 4$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$\frac{5}{3} x - 4 \geq y$

Step 2

Combine $\frac{5}{3}$ and $x$ .

$\frac{5 x}{3} - 4 \geq y$

Step 3

Add $4$ to both sides of the inequality.

$\frac{5 x}{3} \geq y + 4$

Step 4

Multiply both sides by $3$ .

$\frac{5 x}{3} \cdot 3 \geq (y + 4) \cdot 3$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{5 x}{3} \cdot 3 \geq (y + 4) \cdot 3$

Step 5.1.1.2

Rewrite the expression.

$5 x \geq (y + 4) \cdot 3$

$5 x \geq (y + 4) \cdot 3$

$5 x \geq (y + 4) \cdot 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $(y + 4) \cdot 3$ .

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Step 5.2.1.1

Apply the distributive property.

$5 x \geq y \cdot 3 + 4 \cdot 3$

Step 5.2.1.2

Simplify the expression.

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Step 5.2.1.2.1

Move $3$ to the left of $y$ .

$5 x \geq 3 \cdot y + 4 \cdot 3$

Step 5.2.1.2.2

Multiply $4$ by $3$ .

$5 x \geq 3 y + 12$

$5 x \geq 3 y + 12$

$5 x \geq 3 y + 12$

$5 x \geq 3 y + 12$

$5 x \geq 3 y + 12$

Step 6

Divide each term in $5 x \geq 3 y + 12$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x \geq 3 y + 12$ by $5$ .

$\frac{5 x}{5} \geq \frac{3 y}{5} + \frac{12}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{3 y}{5} + \frac{12}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{3 y}{5} + \frac{12}{5}$

$x \geq \frac{3 y}{5} + \frac{12}{5}$

$x \geq \frac{3 y}{5} + \frac{12}{5}$

$x \geq \frac{3 y}{5} + \frac{12}{5}$

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