Question

Solve with absulute value. 2/7 |12-7y| -2 = 7.

Answer 1

The solution to the equation
`\( (2)/(7) \left|12-7y\right| -2 = 7 \)` is
`\( y = -(4)/(7) \)`.

Step-by-step explanation:

To solve the equation, we'll isolate the absolute value term and then solve for
`\( y \)`.

1. Isolating the Absolute Value:

`\[ (2)/(7) \left|12-7y\right| - 2 = 7 \]`

Add 2 to both sides:

`\[ (2)/(7) \left|12-7y\right| = 9 \]`

Multiply both sides by
`\((7)/(2)\)` to get rid of the fraction:

`\[ \left|12-7y\right| = (63)/(2) \]`

2.Setting Up Two Equations:

Since the absolute value can be either positive or negative, we have two cases to consider:

`\[ 12-7y = (63)/(2) \] (Case 1 - Positive)`

Solve for
`\( y \)` in Case 1.

`\[ 12-7y = -(63)/(2) \] (Case 2 - Negative)`

Solve for
`\( y \)` in Case 2.

3. Solving for
`\( y \)`:

After solving both cases, we find
`\( y = -(4)/(7) \)`.

Therefore, the solution to the equation is
`\( y = -(4)/(7) \)`, satisfying both cases.