solve the absolute value equation |3/k-1|=4

Question

can you please show me how you solved it so I can see what I was doing wrong..-thank you

 

Answer 1

The equation is |3/k -1|= 4.

Write the above equation in the form |ax+b| = c where c = 4 ≥0 and it is equivalent to the statement  ax+b = c or ax+b = - c.

Rewrite the equation |3/k -1|= 4 as two equations 3/k -1= 4 or 3/k -1= - 4.

Then solve each equation separately.

Solve the equation 1: 3/k -1= 4.

Add 1 to each side.

3/k -1+1= 4+1

3/k = 5

Multiply each side by k.

5k = 3

Divide each side by 5.

k = 3/5.

Solve the equation 2: 3/k-1= - 4.

Add 1 to each side.

3/k-1+1= - 4+1

3/k = -3

Multiply each side by k.

-3k = 3

Divide each side by negative 3.

-3k/-3 = 3/-3

k = -1.

The solutions of the equation are 3/5 and -1.