Question

which value of k makes $5 - k + 12 = 16$ a true statement? choose 1 answer: a $k = 1$ b $k = 2$ c $k = 3$ d $k = 4$

Explanation:

Step1: Simplify the left - hand side of the equation

First, we simplify the left - hand side of the equation \(5 - k+12\). Combine the constant terms: \(5 + 12=17\), so the equation becomes \(17 - k=16\).

Step2: Solve for \(k\)

We want to isolate \(k\). Subtract 17 from both sides of the equation \(17 - k=16\):
\(-k=16 - 17\)
\(-k=- 1\)
Multiply both sides by - 1 to solve for \(k\): \(k = 1\)

We can also check by substituting the values of \(k\) from the options into the original equation:

• For option A: When \(k = 1\), \(5-1 + 12=4 + 12=16\), which is equal to the right - hand side.
• For option B: When \(k = 2\), \(5-2 + 12=3 + 12=15

eq16\).

• For option C: When \(k = 3\), \(5-3 + 12=2 + 12=14

eq16\).

• For option D: When \(k = 4\), \(5-4 + 12=1 + 12=13

eq16\).

Answer:

A. \(k = 1\)