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Neporo4naja [7]
3 years ago
7

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 Given ⇒ 2(x − 4) + 6x = 9x − 10 Step 1 ⇒ 2x − 8 +

6x = 9x − 10 Step 2 ⇒ 2x + 6x − 8 = 9x − 10 Step 3 ⇒ 8x − 8 = 9x − 10 Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 Step 5 ⇒ 0 − 8 = x − 10 Step 6 ⇒ −8 = x − 10 Step 7 ⇒ −8 + 10 = x − 10 + 10 Step 8 ⇒ 2 = x + 0 Step 9 ⇒ 2 = x Which step in solving this equation is justified by the Distributive Property? A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10 B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10 C) Step 3 ⇒ 8x − 8 = 9x − 10 D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0

Answer:

Step 1

Step-by-step explanation:

You distributed the 2 in 2(x-4) to get 2x-8

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Answer:

x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74

Step-by-step explanation:

Solve for x:

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(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = -434 + 257 (4 - x) - 37 (4 - x)^2

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Divide both sides by -37:

y^2 - (257 y)/37 + 434/37 = 0

Subtract 434/37 from both sides:

y^2 - (257 y)/37 = -434/37

Add 66049/5476 to both sides:

y^2 - (257 y)/37 + 66049/5476 = 1817/5476

Write the left hand side as a square:

(y - 257/74)^2 = 1817/5476

Take the square root of both sides:

y - 257/74 = sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Add 257/74 to both sides:

y = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Substitute back for y = 4 - x:

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Subtract 4 from both sides:

-x = sqrt(1817)/74 - 39/74 or y - 257/74 = -sqrt(1817)/74

Multiply both sides by -1:

x = 39/74 - sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Add 257/74 to both sides:

x = 39/74 - sqrt(1817)/74 or y = 257/74 - sqrt(1817)/74

Substitute back for y = 4 - x:

x = 39/74 - sqrt(1817)/74 or 4 - x = 257/74 - sqrt(1817)/74

Subtract 4 from both sides:

x = 39/74 - sqrt(1817)/74 or -x = -39/74 - sqrt(1817)/74

Multiply both sides by -1:

Answer:  x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74

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