Question

solve for the variable and express the answer on the number line.

1. |3y - 2| + 4 = 10

show your work below your answer. draw the appropriate arrows or points or drag the provided arrows.
(number line with -10 to 10 marked)
answer:

Explanation:

Step1: Isolate the absolute value

Subtract 4 from both sides of the equation \(|3y - 2| + 4 = 10\) to get \(|3y - 2| = 10 - 4\).
\(|3y - 2| = 6\)

Step2: Solve the two cases

Case 1: \(3y - 2 = 6\)
Add 2 to both sides: \(3y = 6 + 2\)
\(3y = 8\)
Divide by 3: \(y = \frac{8}{3}\)

Case 2: \(3y - 2 = -6\)
Add 2 to both sides: \(3y = -6 + 2\)
\(3y = -4\)
Divide by 3: \(y = -\frac{4}{3}\)

Answer:

The solutions are \(y = \frac{8}{3}\) and \(y = -\frac{4}{3}\). To represent on the number line, mark the points \(-\frac{4}{3}\) (which is approximately -1.33) and \(\frac{8}{3}\) (which is approximately 2.67) on the number line.