Make a balanced move so that x is alone on the left, and then rewrite the equation to solve for the value of x.

Question

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 \( 3.33 \).