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 #1 1: solve for x: 3x + 5 = 20 2: solve for x: 2x + 12 = 2 3: solve for x: 5x + 4 = -16 4: solve for x: 5x + 7 = 8 answer choices a: x = -5 b: x = 0 c: x = 2 d: x = 5 e: x = -4 f: x = 1/4 g: x = -1 h: x = 1/5 i: x = 10 type the 4-letter code into the answer box. all caps, no spaces.

Explanation:

Problem 1: Solve \( 3x + 5 = 20 \)

Step 1: Subtract 5 from both sides

To isolate the term with \( x \), we subtract 5 from both sides of the equation.
\( 3x + 5 - 5 = 20 - 5 \)
Simplifying, we get \( 3x = 15 \).

Step 2: Divide by 3

To solve for \( x \), we divide both sides by 3.
\( \frac{3x}{3} = \frac{15}{3} \)
Simplifying, we find \( x = 5 \), which corresponds to option D.

Problem 2: Solve \( 2x + 12 = 2 \)

Step 1: Subtract 12 from both sides

Subtract 12 from both sides to isolate the term with \( x \).
\( 2x + 12 - 12 = 2 - 12 \)
Simplifying, we get \( 2x = -10 \).

Step 2: Divide by 2

Divide both sides by 2 to solve for \( x \).
\( \frac{2x}{2} = \frac{-10}{2} \)
Simplifying, we find \( x = -5 \), which corresponds to option A.

Problem 3: Solve \( 5x + 4 = -16 \)

Step 1: Subtract 4 from both sides

Subtract 4 from both sides to isolate the term with \( x \).
\( 5x + 4 - 4 = -16 - 4 \)
Simplifying, we get \( 5x = -20 \).

Step 2: Divide by 5

Divide both sides by 5 to solve for \( x \).
\( \frac{5x}{5} = \frac{-20}{5} \)
Simplifying, we find \( x = -4 \), which corresponds to option E.

Problem 4: Solve \( 5x + 7 = 8 \)

Answer:

The 4 - letter code is \( \boldsymbol{DAEH} \) (combining the options for each problem: D, A, E, H).