Question

A mathematical equation is shown being solved step-by-step on a black background with peach-colored text. The steps of solving the equation are presented as follows:

The original equation is
5
(
1
+
4
ℎ
)
+
2
ℎ
=
27
5(1+4h)+2h=27.
Expanding the equation, it becomes
5
+
20
ℎ
+
2
ℎ
=
27
5+20h+2h=27.
The terms with
ℎ
h are combined to give
27
ℎ
=
27
27h=27.
Both sides are divided by 27, resulting in
ℎ
=
1
h=1.

Find the mistake

Answer 1

Let's review the steps in solving the equation \( 5(1 + 4h) + 2h = 27 \):

1. **Original Equation**:
\[
5(1 + 4h) + 2h = 27
\]

2. **Expanding**:
\[
5 \cdot 1 + 5 \cdot 4h + 2h = 27 \implies 5 + 20h + 2h = 27
\]

3. **Combining Like Terms**:
\[
5 + 22h = 27
\]
(Here is where the mistake occurs; it incorrectly states \( 27h = 27 \), which is wrong.)

4. **Solving for \( h \)**:
Now, subtract 5 from both sides:
\[
22h = 27 - 5 \implies 22h = 22
\]
Now, divide both sides by 22:
\[
h = 1
\]

The mistake is in the step where it incorrectly states that after combining like terms, the equation becomes \( 27h = 27 \). The correct combination of terms leads to \( 22h = 22 \).