Question

Solve the following absolute value equations. Show the solution set and check your answers. |0.3-3/5k|-0.4=1.2

Answer 1

**The equation is not clear, so I have provided both options**

Option 1

`\left|0.3-(3)/(5)k\right|-0.4=1.2`

`\implies \left|0.3-(3)/(5)k\right|=1.6`

Solution 1

`\implies 0.3-(3)/(5)k=1.6`

`\implies -(3)/(5)k=1.3`

`\implies k=-(13)/(6)`

Solution 2

`\implies -(0.3-(3)/(5)k)=1.6`

`\implies -0.3+(3)/(5)k=1.6`

`\implies (3)/(5)k=1.9`

`\implies k=(19)/(6)`

Option 2

`\left|0.3-(3)/(5k)\right|-0.4=1.2`

`\implies \left|0.3-(3)/(5k)\right|=1.6`

Solution 1

`\implies 0.3-(3)/(5k)=1.6`

`\implies -(3)/(5k)=1.3`

`\implies -3=6.5k`

`\implies k=-(6)/(13)`

Solution 2

`\implies -(0.3-(3)/(5k))=1.6`

`\implies -0.3+(3)/(5k)=1.6`

`\implies (3)/(5k)=1.9`

`\implies 3=9.5k`

`\implies k=(6)/(19)`