a) $$ \frac{7 g-8}{3}=\frac{3+6 g}{6} $$

Question

UpStudy AI · Accepted Answer

We start with the equation

$$
\frac{7g-8}{3}=\frac{3+6g}{6}.
$$

**Step 1:** Multiply both sides by $$6$$ (the least common multiple of $$3$$ and $$6$$):

$$
6\cdot\frac{7g-8}{3}=6\cdot\frac{3+6g}{6}.
$$

This simplifies to

$$
2(7g-8)=3+6g.
$$

**Step 2:** Distribute on the left side:

$$
14g-16=3+6g.
$$

**Step 3:** Subtract $$6g$$ from both sides to gather the $$g$$-terms:

$$
14g-6g-16=3,
$$

which simplifies to

$$
8g-16=3.
$$

**Step 4:** Add $$16$$ to both sides to isolate the term with $$g$$:

$$
8g=3+16,
$$

so

$$
8g=19.
$$

**Step 5:** Divide both sides by $$8$$:

$$
g=\frac{19}{8}.
$$
$$ g = \frac{19}{8} $$

a) \( \frac{7 g-8}{3}=\frac{3+6 g}{6} \)