Question

-2(3a - 8) = \frac{2}{3}(3a - 60)

Explanation:

Step1: Eliminate fraction by multiplying both sides by 3

Multiply each term by 3 to get rid of the denominator.
$$3\times(-2(3a - 8)) = 3\times\frac{2}{3}(3a - 60)$$
Simplify:
$$-6(3a - 8) = 2(3a - 60)$$

Step2: Distribute both sides

Apply the distributive property (\(a(b - c) = ab - ac\)) to both sides.
Left side: \(-6\times3a + (-6)\times(-8) = -18a + 48\)
Right side: \(2\times3a + 2\times(-60) = 6a - 120\)
Equation becomes:
$$-18a + 48 = 6a - 120$$

Step3: Move variable terms to one side

Subtract \(6a\) from both sides:
$$-18a - 6a + 48 = -120$$
Simplify:
$$-24a + 48 = -120$$

Step4: Move constant terms to the other side

Subtract 48 from both sides:
$$-24a = -120 - 48$$
Simplify:
$$-24a = -168$$

Step5: Solve for \(a\)

Divide both sides by \(-24\):
$$a = \frac{-168}{-24}$$
Simplify the fraction:
$$a = 7$$

Answer:

\(a = 7\)