Algebra-2

To solve the equation 18 - 2|7x - 1| = -10, follow these steps:

Step 1: Isolate the Absolute Value

First, subtract 18 from both sides:

-2|7x - 1| = -10 - 18

-2|7x - 1| = -28

Next, divide both sides by -2:

|7x - 1| =

|7x - 1| = 14

 

Step 2: Set Up Cases for Absolute Value

Now we can set up two cases based on the definition of absolute value:

1.Case 1:

7x - 1 = 14

 

2.Case 2:

7x - 1 = -14

 

Step 3: Solve Each Case

For Case 1:

7x - 1 = 14

Add 1 to both sides:

7x = 14 + 1

7x = 15

Now, divide by 7:

 

For Case 2:

7x - 1 = -14

Add 1 to both sides:

7x = -14 + 1

7x = -13

Now, divide by 7:

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