SOLUTION: Solve |7x - 4| = 10. Be sure to list all answers together. SHOW ALL WORK THANK YOU

Algebra ->  Graphs -> SOLUTION: Solve |7x - 4| = 10. Be sure to list all answers together. SHOW ALL WORK THANK YOU       Log On


   

Question 118913: Solve |7x - 4| = 10. Be sure to list all answers together.
SHOW ALL WORK
THANK YOU
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%287x-4%29=10 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

7x-4=-10 or 7x-4=10 Set the expression 7x-4 equal to the original value 10 and it's opposite -10




Now lets focus on the first equation 7x-4=-10


7x=-10%2B4Add 4 to both sides


7x=-6 Combine like terms on the right side


x=%28-6%29%2F%287%29 Divide both sides by 7 to isolate x



x=-6%2F7 Reduce






Now lets focus on the second equation 7x-4=10



7x=10%2B4Add 4 to both sides


7x=14 Combine like terms on the right side


x=%2814%29%2F%287%29 Divide both sides by 7 to isolate x



x=2 Divide





So the solutions to abs%287x-4%29=10 are:

x=-6%2F7 and x=2



Notice if we graph y=abs%287x-4%29 and y=10 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-15%2C15%2C-15%2C15%2Cabs%287x-4%29%2C10%29 Graph of y=abs%287x-4%29 (red) and y=10(green)

and we can see the two graphs intersect at x=-6%2F7 and x=2. So this verifies our answer.