MATH SOLVE

4 months ago

Q:
# Use the drop-down menus to choose steps in order to correctly solve 5(z + 6) β 2 = 9z for z.

Accepted Solution

A:

Solve for z:

5 (z + 6) - 2 = 9 z

5 (z + 6) = 5 z + 30:

5 z + 30 - 2 = 9 z

Add like terms. 30 - 2 = 28:

5 z + 28 = 9 z

Subtract 9 z from both sides:

(5 z - 9 z) + 28 = 9 z - 9 z

5 z - 9 z = -4 z:

-4 z + 28 = 9 z - 9 z

9 z - 9 z = 0:

28 - 4 z = 0

Subtract 28 from both sides:

(28 - 28) - 4 z = -28

28 - 28 = 0:

-4 z = -28

Divide both sides of -4 z = -28 by -4:

(-4 z)/(-4) = (-28)/(-4)

(-4)/(-4) = 1:

z = (-28)/(-4)

The gcd of 28 and -4 is 4, so (-28)/(-4) = (-(4Γ7))/(4 (-1)) = 4/4Γ(-7)/(-1) = (-7)/(-1):

z = (-7)/(-1)

(-7)/(-1) = (-1)/(-1)Γ7 = 7:

Answer:Β z = 7

5 (z + 6) - 2 = 9 z

5 (z + 6) = 5 z + 30:

5 z + 30 - 2 = 9 z

Add like terms. 30 - 2 = 28:

5 z + 28 = 9 z

Subtract 9 z from both sides:

(5 z - 9 z) + 28 = 9 z - 9 z

5 z - 9 z = -4 z:

-4 z + 28 = 9 z - 9 z

9 z - 9 z = 0:

28 - 4 z = 0

Subtract 28 from both sides:

(28 - 28) - 4 z = -28

28 - 28 = 0:

-4 z = -28

Divide both sides of -4 z = -28 by -4:

(-4 z)/(-4) = (-28)/(-4)

(-4)/(-4) = 1:

z = (-28)/(-4)

The gcd of 28 and -4 is 4, so (-28)/(-4) = (-(4Γ7))/(4 (-1)) = 4/4Γ(-7)/(-1) = (-7)/(-1):

z = (-7)/(-1)

(-7)/(-1) = (-1)/(-1)Γ7 = 7:

Answer:Β z = 7