Question

how many solutions does the following equation have?
$3z + 9 + 14z = 4z + 5$
choose 1 answer:
a no solutions
b exactly one solution
c infinitely many solutions

Explanation:

Step1: Combine like terms on left

$3z + 14z + 9 = 17z + 9$
Equation becomes: $17z + 9 = 4z + 5$

Step2: Isolate z terms on left

Subtract $4z$ from both sides:
$17z - 4z + 9 = 5$
$13z + 9 = 5$

Step3: Isolate constant terms on right

Subtract 9 from both sides:
$13z = 5 - 9$
$13z = -4$

Step4: Solve for z

Divide both sides by 13:
$z = \frac{-4}{13}$

Answer:

B. Exactly one solution