Pre-Algebra Examples

$(\sqrt{63 (25 \cdot 4 - 37)}) - 49 x > 21 (3 - 7 y)$

Step 1

Write in $y = m x + b$ form.

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Step 1.1

Solve for $y$ .

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Step 1.1.1

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

$21 (3 - 7 y) < \sqrt{63 (25 \cdot 4 - 37)} - 49 x$

Step 1.1.2

Simplify.

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Step 1.1.2.1

Multiply $25$ by $4$ .

$21 (3 - 7 y) < \sqrt{63 (100 - 37)} - 49 x$

Step 1.1.2.2

Subtract $37$ from $100$ .

$21 (3 - 7 y) < \sqrt{63 \cdot 63} - 49 x$

Step 1.1.2.3

Multiply $63$ by $63$ .

$21 (3 - 7 y) < \sqrt{3969} - 49 x$

Step 1.1.3

Divide each term in $21 (3 - 7 y) < \sqrt{3969} - 49 x$ by $21$ and simplify.

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Step 1.1.3.1

Divide each term in $21 (3 - 7 y) < \sqrt{3969} - 49 x$ by $21$ .

$\frac{21 (3 - 7 y)}{21} < \frac{\sqrt{3969}}{21} + \frac{- 49 x}{21}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $21$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{21 (3 - 7 y)}{21} < \frac{\sqrt{3969}}{21} + \frac{- 49 x}{21}$

Step 1.1.3.2.1.2

Divide $3 - 7 y$ by $1$ .

$3 - 7 y < \frac{\sqrt{3969}}{21} + \frac{- 49 x}{21}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Simplify each term.

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Step 1.1.3.3.1.1

Simplify the numerator.

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Step 1.1.3.3.1.1.1

Rewrite $3969$ as $63^{2}$ .

$3 - 7 y < \frac{\sqrt{63^{2}}}{21} + \frac{- 49 x}{21}$

Step 1.1.3.3.1.1.2

Pull terms out from under the radical, assuming positive real numbers.

$3 - 7 y < \frac{63}{21} + \frac{- 49 x}{21}$

Step 1.1.3.3.1.2

Divide $63$ by $21$ .

$3 - 7 y < 3 + \frac{- 49 x}{21}$

Step 1.1.3.3.1.3

Cancel the common factor of $- 49$ and $21$ .

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Step 1.1.3.3.1.3.1

Factor $7$ out of $- 49 x$ .

$3 - 7 y < 3 + \frac{7 (- 7 x)}{21}$

Step 1.1.3.3.1.3.2

Cancel the common factors.

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Step 1.1.3.3.1.3.2.1

Factor $7$ out of $21$ .

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

Step 1.1.3.3.1.3.2.2

Cancel the common factor.

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

Step 1.1.3.3.1.3.2.3

Rewrite the expression.

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

Step 1.1.3.3.1.4

Move the negative in front of the fraction.

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

Step 1.1.4

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

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Step 1.1.4.1

Subtract $3$ from both sides of the inequality.

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

Step 1.1.4.2

Combine the opposite terms in $3 - \frac{7 x}{3} - 3$ .

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Step 1.1.4.2.1

Subtract $3$ from $3$ .

$- 7 y < - \frac{7 x}{3} + 0$

Step 1.1.4.2.2

Add $- \frac{7 x}{3}$ and $0$ .

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

Step 1.1.5

Divide each term in $- 7 y < - \frac{7 x}{3}$ by $- 7$ and simplify.

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Step 1.1.5.1

Divide each term in $- 7 y < - \frac{7 x}{3}$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} > \frac{- \frac{7 x}{3}}{- 7}$

Step 1.1.5.2

Simplify the left side.

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Step 1.1.5.2.1

Cancel the common factor of $- 7$ .

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Step 1.1.5.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} > \frac{- \frac{7 x}{3}}{- 7}$

Step 1.1.5.2.1.2

Divide $y$ by $1$ .

$y > \frac{- \frac{7 x}{3}}{- 7}$

Step 1.1.5.3

Simplify the right side.

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Step 1.1.5.3.1

Multiply the numerator by the reciprocal of the denominator.

$y > - \frac{7 x}{3} \cdot \frac{1}{- 7}$

Step 1.1.5.3.2

Cancel the common factor of $7$ .

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Step 1.1.5.3.2.1

Move the leading negative in $- \frac{7 x}{3}$ into the numerator.

$y > \frac{- 7 x}{3} \cdot \frac{1}{- 7}$

Step 1.1.5.3.2.2

Factor $7$ out of $- 7 x$ .

$y > \frac{7 (- x)}{3} \cdot \frac{1}{- 7}$

Step 1.1.5.3.2.3

Factor $7$ out of $- 7$ .

$y > \frac{7 (- x)}{3} \cdot \frac{1}{7 (- 1)}$

Step 1.1.5.3.2.4

Cancel the common factor.

$y > \frac{7 (- x)}{3} \cdot \frac{1}{7 \cdot - 1}$

Step 1.1.5.3.2.5

Rewrite the expression.

$y > \frac{- x}{3} \cdot \frac{1}{- 1}$

Step 1.1.5.3.3

Multiply $\frac{- x}{3}$ by $\frac{1}{- 1}$ .

$y > \frac{- x}{3 \cdot - 1}$

Step 1.1.5.3.4

Multiply $3$ by $- 1$ .

$y > \frac{- x}{- 3}$

Step 1.1.5.3.5

Dividing two negative values results in a positive value.

$y > \frac{x}{3}$

Step 1.2

Reorder terms.

$y > \frac{1}{3} x$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{1}{3}$

$b = 0$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{3}$

y-intercept: $(0, 0)$

Slope: $\frac{1}{3}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{3} x$ .

$y > \frac{1}{3} x$

Step 4