Question

Start by multiplying the left side of the equation by 2 to get rid of the fraction on the left side of the equation.
2
3
​
(4+3b)
=
2+2b

2 ·
2
3
​
(4+3b)
=
2 · (2+2b)

(4+3b)
=
?

Answer 1

To solve the equation by multiplying both sides by 2, we will start with:

\[
\frac{2}{3}(4 + 3b) = 2 + 2b
\]

Multiply both sides by 2:

\[
2 \cdot \frac{2}{3}(4 + 3b) = 2 \cdot (2 + 2b)
\]

This simplifies to:

\[
\frac{4}{3}(4 + 3b) = 4 + 4b
\]

Now, to get rid of the fraction, we multiply both sides by 3. The equation then becomes:

\[
4(4 + 3b) = 3(4 + 4b)
\]

Now, let's expand both sides:

\[
16 + 12b = 12 + 12b
\]

Next, we'll isolate the variable. We can subtract \(12b\) from both sides:

\[
16 = 12
\]

This is an inconsistency, which implies that there is no solution to the original equation since we derived a contradiction.

Thus, the final result of the left side simplifies out as demonstrated, but there is no solution when fully solved—indicating the two sides are unequal.