Algebra Examples

$3 x + 6 y \leq 64 x + y \leq 8$

Step 1

Solve $3 x + 6 y \leq 64 x + y$ for $y$ .

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Step 1.1

Move all terms containing $y$ to the left side of the inequality.

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Step 1.1.1

Subtract $y$ from both sides of the inequality.

$3 x + 6 y - y \leq 64 x$

Step 1.1.2

Subtract $y$ from $6 y$ .

$3 x + 5 y \leq 64 x$

Step 1.2

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

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Step 1.2.1

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

$5 y \leq 64 x - 3 x$

Step 1.2.2

Subtract $3 x$ from $64 x$ .

$5 y \leq 61 x$

Step 1.3

Divide each term in $5 y \leq 61 x$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 y \leq 61 x$ by $5$ .

$\frac{5 y}{5} \leq \frac{61 x}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} \leq \frac{61 x}{5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{61 x}{5}$

Step 2

Subtract $64 x$ from both sides of the inequality.

$y \leq 8 - 64 x$

Step 3

Find the intersection of $y \leq \frac{61 x}{5}$ and $y \leq 8 - 64 x$ .

$y \leq N o (Min i m u m)$

Step 4