Question

Brad tried to solve 0.3(6b–2)=
–
0.2(7b–2). Here is his work:
1.8b–0.6
=
–
1.4b–0.4 Step 1
3.2b–0.6
=
–
0.4 Step 2
3.2b
= 0.2 Step 3
b
= 0.0625 Step 4
Did Brad solve the equation correctly?

Answer 1

Let's start by examining the original equation that Brad aimed to solve:

\[
0.3(6b - 2) = -0.2(7b - 2)
\]

Now we will expand both sides of the equation:

**Left Side:**
\[
0.3(6b - 2) = 0.3 \cdot 6b - 0.3 \cdot 2 = 1.8b - 0.6
\]

**Right Side:**
\[
-0.2(7b - 2) = -0.2 \cdot 7b + 0.2 \cdot 2 = -1.4b + 0.4
\]

Now we have:
\[
1.8b - 0.6 = -1.4b + 0.4
\]

Next, we will rearrange the equation to isolate \(b\). Adding \(1.4b\) to both sides gives:
\[
1.8b + 1.4b - 0.6 = 0.4
\]
\[
3.2b - 0.6 = 0.4
\]

Now, let's add \(0.6\) to both sides:
\[
3.2b = 0.4 + 0.6
\]
\[
3.2b = 1.0
\]

Now, we divide both sides by \(3.2\):
\[
b = \frac{1.0}{3.2} = 0.3125
\]

Thus, the correct value for \(b\) is:
\[
b = 0.3125
\]

Brad reached a different answer, \(0.0625\), at Step 4, meaning he made an error in his solution.

Therefore, Brad did not solve the equation correctly.