Question

7. The steps below show Cam's work in solving

an equation. Circle the line where he makes a
mistake. Then, find the correct solution to the
equation.
10-2x = 14x + 2
10 = 16x + 2
12 = 16x
3
X
x = 4

Answer 1

Answer: x = 5/9

Step-by-step explanation:

The mistake in Cam's work is in the second step:

10 - 2x = 14x + 2

Cam incorrectly added 2x to both sides of the equation. The correct step would be to subtract 2x from both sides of the equation:

10 - 2x - 2x = 14x + 2 - 2x

This would result in:

10 - 4x = 14x

Now, you can continue to solve for x:

10 - 4x = 14x

Subtract 14x from both sides:

10 - 4x - 14x = 14x - 14x

This simplifies to:

10 - 18x = 0

Now, add 18x to both sides:

10 - 18x + 18x = 0 + 18x

10 = 18x

Finally, divide by 18 to isolate x:

10/18 = 18x/18

5/9 = x

Answer 2

`\sf x = (1)/(2)`

Explanation:

Cam makes a mistake on the line 12 = 16x. He should have subtracted 2 from both sides of the equation instead of adding 2 to the left side and subtracting 2 to right sides:

The correct solution to the equation is:

`\sf 10-2x = 14x + 2`

Add 2x on both sides, we get

`\sf 10 = 16x + 2`

Subtract 2 on both sides, we get

`\sf 8 = 16x`

Divide both sides by 16, we get

`\sf x = (1)/(2)`

Therefore, the correct solution is:

`\sf x = (1)/(2)`