Question

1. Solve: -6x = 354

2. x/2 = 12
3. (-1/3) b = 9
4. -13x = -52
5. Sierra bought 6 shirts for $67.50, how much did she pay for each shirt if they all cost the same?

Answer 1

1) x = 354/-6.
x = -59

2) x = 12*2 = 24

3) b = 9(-3) = -27

4) x = -52/-13 = 4

5) 6 shirts, $67.50
1 shirt, $67.50 divided by 6.
1 shirt, $11.25

Answer 2

1. Solve for x:

-6 x = 354

Divide both sides of -6 x = 354 by -6:

(-6 x)/(-6) = 354/(-6)

(-6)/(-6) = 1:

x = 354/(-6)

The gcd of 354 and -6 is 6, so 354/(-6) = (6×59)/(6 (-1)) = 6/6×59/(-1) = 59/(-1):

x = 59/(-1)

Multiply numerator and denominator of 59/(-1) by -1:

Answer: x = -59

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2. Solve for x:

x/2 = 12

Multiply both sides of x/2 = 12 by 2:

(2 x)/2 = 2×12

(2 x)/2 = 2/2×x = x:

x = 2×12

2×12 = 24:

Answer: x = 24

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Solve for b:

-b/3 = 9

Multiply both sides of -b/3 = 9 by -3:

(-3 (-b))/3 = -3×9

-3×(-1)/3 = (-3 (-1))/3:

(-3 (-1))/3 b = -3×9

(-3)/3 = (3 (-1))/3 = -1:

--1 b = -3×9

(-1)^2 = 1:

b = -3×9

-3×9 = -27:

Answer: b = -27

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Solve for x:

-13 x = -52

Divide both sides of -13 x = -52 by -13:

(-13 x)/(-13) = (-52)/(-13)

(-13)/(-13) = 1:

x = (-52)/(-13)

The gcd of -52 and -13 is -13, so (-52)/(-13) = (-13×4)/(-13×1) = (-13)/(-13)×4 = 4:

Answer: x = 4

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5. Simply divide by 6

$67.50/6= $11.25