Answer:
E. distributive property of multiplication over addition.
Step-by-step explanation:
Expand the following:
(-7 x - 8 = 3 (2 x + 3), Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Distribute 3 over 2 x + 3.
3 (2 x + 3) = 3 (2 x) + 3 3:
(-7 x - 8 = 3 2 x + 3 3, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Multiply 3 and 3 together.
3×3 = 9:
(-7 x - 8 = 3 2 x + 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Multiply 3 and 2 together.
3×2 = 6:
(-7 x - 8 = 6 x + 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Move terms with x to the left hand side.
Subtract 6 x from both sides:
((-7 x - 6 x) - 8 = (6 x - 6 x) + 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Combine like terms in -7 x - 6 x.
-7 x - 6 x = -13 x:
(-13 x - 8 = (6 x - 6 x) + 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Look for the difference of two identical terms.
6 x - 6 x = 0:
(-13 x - 8 = 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Isolate terms with x to the left hand side.
Add 8 to both sides:
((8 - 8) - 13 x = 8 + 9, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Look for the difference of two identical terms.
8 - 8 = 0:
(-13 x = 9 + 8, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Evaluate 9 + 8.
9 + 8 = 17:
(-13 x = 17, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -13 x = 17 by -13:
((-13 x)/(-13) = 17/(-13), Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Any nonzero number divided by itself is one.
(-13)/(-13) = 1:
(x = 17/(-13), Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Simplify the sign of 17/(-13).
Multiply numerator and denominator of 17/(-13) by -1:
(x = (-17)/13, Sort[True], -7 x - 8 = 6 x + 9)
Hint: | Move terms with x to the left hand side.
Subtract 6 x from both sides:
(x = -17/13, Sort[True], (-7 x - 6 x) - 8 = (6 x - 6 x) + 9)
Hint: | Combine like terms in -7 x - 6 x.
-7 x - 6 x = -13 x:
(x = -17/13, Sort[True], -13 x - 8 = (6 x - 6 x) + 9)
Hint: | Look for the difference of two identical terms.
6 x - 6 x = 0:
(x = -17/13, Sort[True], -13 x - 8 = 9)
Hint: | Isolate terms with x to the left hand side.
Add 8 to both sides:
(x = -17/13, Sort[True], (8 - 8) - 13 x = 8 + 9)
Hint: | Look for the difference of two identical terms.
8 - 8 = 0:
(x = -17/13, Sort[True], -13 x = 9 + 8)
Hint: | Evaluate 9 + 8.
9 + 8 = 17:
(x = -17/13, Sort[True], -13 x = 17)
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -13 x = 17 by -13:
(x = -17/13, Sort[True], (-13 x)/(-13) = 17/(-13))
Hint: | Any nonzero number divided by itself is one.
(-13)/(-13) = 1:
(x = -17/13, Sort[True], x = 17/(-13))
Hint: | Simplify the sign of 17/(-13).
Multiply numerator and denominator of 17/(-13) by -1:
Answer: (x = -17/13, Sort[True], x = (-17)/13)
