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2 years ago

Sasha is solving a multi-step equation. Her first step is shown below.

Mathematics

1 answer:

lesantik [10]2 years ago

6 0

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)

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