Question

micah richard
advanced math
homework 6

1. $-7(m - 9) - 2m = 12$
2. $16 = 9 - 4(2r + 7) - 1$
3. $-8(4n - 1) = 2(9 - 3n)$
4. $-\frac{4}{3}(12v - 18 + 32) = -8(7 + 2v)$
5. $1 = \frac{x\cdot 2\pi r}{800}$ solve for $r$
6. $\frac{3y - x}{3 - 2x} = -9$ solve for $y$

Explanation:

Problem 1: Solve for $m$

Step1: Expand the parentheses

$-7(m-9) - 2m = 12$
$-7m + 63 - 2m = 12$

Step2: Combine like terms

$-9m + 63 = 12$

Step3: Isolate the variable term

$-9m = 12 - 63$
$-9m = -51$

Step4: Solve for $m$

$m = \frac{-51}{-9} = \frac{17}{3}$

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Problem 3: Solve for $r$

Step1: Simplify constants on right

$16 = 9 - 4(2r+7) - 1$
$16 = 8 - 4(2r+7)$

Step2: Expand the parentheses

$16 = 8 - 8r - 28$

Step3: Combine like terms

$16 = -20 - 8r$

Step4: Isolate the variable term

$8r = -20 - 16$
$8r = -36$

Step5: Solve for $r$

$r = \frac{-36}{8} = -\frac{9}{2}$

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Problem 5: Solve for $n$

Step1: Expand both sides

$-8(4n-1) = 2(9-3n)$
$-32n + 8 = 18 - 6n$

Step2: Isolate variable terms

$-32n + 6n = 18 - 8$
$-26n = 10$

Step3: Solve for $n$

$n = \frac{10}{-26} = -\frac{5}{13}$

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Problem 7: Solve for $v$

Step1: Simplify inside left parentheses

$-\frac{4}{3}(12v - 18 + 32) = -8(7+2v)$
$-\frac{4}{3}(12v + 14) = -8(7+2v)$

Step2: Expand both sides

$-\frac{4}{3}(12v) - \frac{4}{3}(14) = -56 - 16v$
$-16v - \frac{56}{3} = -56 - 16v$

Step3: Analyze the equation

Add $16v$ to both sides:
$-\frac{56}{3} = -56$
This is a false statement, so there is no solution.

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Problem 9: Solve for $r$

Step1: Multiply both sides by 360

$1 = \frac{x \cdot 2 \pi r}{360}$
$360 = 2 \pi x r$

Step2: Isolate $r$

$r = \frac{360}{2 \pi x} = \frac{180}{\pi x}$

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Problem 11: Solve for $y$

Step1: Multiply both sides by denominator

$\frac{3y - x}{3-2x} = 4$
$3y - x = 4(3-2x)$

Step2: Expand the right side

$3y - x = 12 - 8x$

Step3: Isolate the $y$ term

$3y = 12 - 8x + x$
$3y = 12 - 7x$

Step4: Solve for $y$

$y = \frac{12 - 7x}{3}$

Answer:

1. $m = \frac{17}{3}$
2. $r = -\frac{9}{2}$
3. $n = -\frac{5}{13}$
4. No solution
5. $r = \frac{180}{\pi x}$
6. $y = \frac{12 - 7x}{3}$