Question

topic: equations and inequalities and absolute value
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (includ
solve for $y$:
$|6y - 3| + 8 = 35$
$\bigcirc$ $y = - 5$
$\bigcirc$ $y = 5$ or $y = - 4$
$\bigcirc$ $y = 5$
$\bigcirc$ $y = 5$ 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 linear equations

Absolute value equals positive/negative 27.
$$6y - 3 = 27 \quad \text{or} \quad 6y - 3 = -27$$

Step3: Solve first linear equation

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

Step4: Solve second linear equation

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

Answer:

y = 5 or y = - 4