Answer:
[tex]w=-1/5\text{ or } 3[/tex]
Step-by-step explanation:
We have the equation:
[tex]-2|5w-7|+9=-7[/tex]
Let's first isolate the absolute value. Subtract 9 from both sides:
[tex]-2|5w-7|=-16[/tex]
Divide both sides by -2:
[tex]|5w-7|=8[/tex]
Now, we can split them into two cases. By the definition of absolute value:
[tex]5w-7=8\text{ or } -(5w-7)=8[/tex]
Let's do each case individually.
Case 1:
We have:
[tex]5w-7=8[/tex]
Add 7 to both sides:
[tex]5w=15[/tex]
Divide both sides by 5:
[tex]w=3[/tex]
Case 2:
We have:
[tex]-(5w-7)=8[/tex]
Divide both sides by -1:
[tex]5w-7=-8[/tex]
Add 7 to both sides:
[tex]5w=-1[/tex]
Divide both sides by 5:
[tex]w=-1/5[/tex]
So, our answers are:
[tex]w=-1/5\text{ or } 3[/tex]
And we're done!
