Question

solve for y: |6y - 3| + 8 = 35 options: y = 5 or y = -4; y = -5; y = 5; y = 5 or y = -\frac{20}{3}

Explanation:

Step1: Isolate the absolute value

Subtract 8 from both sides.
$$|6y - 3| = 35 - 8$$
$$|6y - 3| = 27$$

Step2: Split into two cases

Absolute value gives two equations: positive and negative.
$$6y - 3 = 27 \quad \text{or} \quad 6y - 3 = -27$$

Step3: Solve first equation

Add 3, then divide by 6.
$$6y = 27 + 3$$
$$6y = 30$$
$$y = \frac{30}{6} = 5$$

Step4: Solve second equation

Add 3, then divide by 6.
$$6y = -27 + 3$$
$$6y = -24$$
$$y = \frac{-24}{6} = -4$$

Answer:

$y = 5$ or $y = -4$ (corresponding to the option: $\boldsymbol{y = 5 \text{ or } y = -4}$)