Question

1. using only step 1 followed by step 2 below, amir correctly solved a linear equation. step 1: subtract 16 from both sides of the equation. step 2: multiply both sides of the resulting equation by 5. one of the following equations is the equation that amir solved. which one? f. \\(\frac{1}{5}n - 16 = 14\\) g. \\(\frac{1}{5}n - 14 = 16\\) h. \\(\frac{1}{5}n + 16 = 14\\) j. \\(5n - 16 = 14\\) k. \\(5n + 14 = 16\\)

Explanation:

Step1: Test Option F with Step1

Subtract 16 from both sides:
$\frac{1}{5}n - 16 - 16 = 14 - 16$
$\frac{1}{5}n - 32 = -2$
Step2 would not isolate $n$, so F is invalid.

Step2: Test Option G with Step1

Subtract 16 from both sides:
$\frac{1}{5}n - 14 - 16 = 16 - 16$
$\frac{1}{5}n - 30 = 0$
Step2 would not isolate $n$, so G is invalid.

Step3: Test Option H with Step1

Subtract 16 from both sides:
$\frac{1}{5}n + 16 - 16 = 14 - 16$
$\frac{1}{5}n = -2$

Step4: Apply Step2 to H's result

Multiply both sides by 5:
$5 \times \frac{1}{5}n = 5 \times (-2)$
$n = -10$
This matches the required steps, so H is valid.

Step5: Test Option J with Step1

Subtract 16 from both sides:
$5n - 16 - 16 = 14 - 16$
$5n - 32 = -2$
Step2 would overcomplicate isolating $n$, so J is invalid.

Step6: Test Option K with Step1

Subtract 16 from both sides:
$5n + 14 - 16 = 16 - 16$
$5n - 2 = 0$
Step2 would overcomplicate isolating $n$, so K is invalid.

Answer:

H. $\frac{1}{5}n + 16 = 14$