Question

Make a balanced move so that x is alone on the left, and then rewrite the equation to solve for the value of x.
Zoe's miles
=
James's miles

20+6x
=
40−4x
+
4x
+
4x

20 + 10x
=
40
−
20
−
20

10x
=
20

x
=

Answer 1

To isolate \( x \) and solve the equation step by step, we can start from the balanced equation you provided:

1. The original equation is:

\[
20 + 10x = 40 - 4x + 4x + 4x
\]

2. Simplify the right side of the equation:

\[
20 + 10x = 40 - 4x + 4x + 4x = 40 + 4x
\]

3. Set up the equation again:

\[
20 + 10x = 40 + 4x
\]

4. Now, we want to isolate \( x \). To do this, we can subtract \( 4x \) from both sides:

\[
20 + 10x - 4x = 40
\]

Which simplifies to:

\[
20 + 6x = 40
\]

5. Next, subtract 20 from both sides:

\[
6x = 40 - 20
\]

This simplifies to:

\[
6x = 20
\]

6. Finally, divide both sides by 6 to solve for \( x \):

\[
x = \frac{20}{6} = \frac{10}{3} \approx 3.33
\]

So, the value of \( x \) is:

\[
x = \frac{10}{3}
\] or approximately \( 3.33 \).