Question

can you solve each equation and type the correct code? please remember to type * in all caps with no spaces. you must show all work in order to earn credit! puzzle #3 1: solve for x: -8(x -1) = 32 2: solve for x: 2(x + 4) = 14 3: solve for x: 3(x +3) = -15 4: solve for x: -2(4x - 3) = 2 answer choices a: x = 1/2 b: x = 3 c: infinite solutions d: x = -3 e: x = -8 f: x = 1/3 g: no solution h: x = -5 i: x = 2 type the 4-letter code into the answer box. all caps. no spaces.

Explanation:

Problem 1: Solve \(-8(x - 1) = 32\)

Step 1: Divide both sides by -8

To isolate the term with \(x\), divide both sides of the equation by \(-8\).
\(\frac{-8(x - 1)}{-8} = \frac{32}{-8}\)
Simplifying, we get \(x - 1 = -4\).

Step 2: Add 1 to both sides

To solve for \(x\), add 1 to both sides of the equation.
\(x - 1 + 1 = -4 + 1\)
Simplifying, we get \(x = -3\).
This corresponds to option D.

Problem 2: Solve \(2(x + 4) = 14\)

Step 1: Divide both sides by 2

To isolate the term with \(x\), divide both sides of the equation by 2.
\(\frac{2(x + 4)}{2} = \frac{14}{2}\)
Simplifying, we get \(x + 4 = 7\).

Step 2: Subtract 4 from both sides

To solve for \(x\), subtract 4 from both sides of the equation.
\(x + 4 - 4 = 7 - 4\)
Simplifying, we get \(x = 3\).
This corresponds to option B.

Problem 3: Solve \(3(x + 3) = -15\)

Step 1: Divide both sides by 3

To isolate the term with \(x\), divide both sides of the equation by 3.
\(\frac{3(x + 3)}{3} = \frac{-15}{3}\)
Simplifying, we get \(x + 3 = -5\).

Step 2: Subtract 3 from both sides

To solve for \(x\), subtract 3 from both sides of the equation.
\(x + 3 - 3 = -5 - 3\)
Simplifying, we get \(x = -8\).
This corresponds to option E.

Problem 4: Solve \(-2(4x - 3) = 2\)

Answer:

DBEA