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divide both sides by -3 first, which gives us |2x+6| = 4 write equations for the two cases: (2x+6) = 4 and (2x+6) = -4 solve both equations for x.
ok. I have a question for absolute value. Can there ever be negative in your answer?
Wouldn't I have to divide 2x by 2 and 4 by two in order to get x by itself?
not quite, you want to subtract 6 from both sides first ok, we have two equations, let's start with the first one: (2x+6) = 4 first step, we want to subtract 6 from both sides 2x + 6 - 6 = 4 -6 = -2 2x = -2 x = -1 now, let's move to the second equation (2x+6) = -4 2x + 6 - 6 = -4 - 6 = -10 2x = -10 x = -5
so the answer is x=-1 and x=-5? I thought the answer couldn't have negatives in it?
we're solving for x, x can be either positive, negative, or 0
Ok. Can you please help me solve this problem too. Your a lot of help. Solve for x: |x - 2| + 10 = 12 x = 0 and x = 4 x = -4 and x = 0 x = -20 and x = 4 No solution
subtract 10 from both sides first then write out the two equations...
is the answer x=4 and x=0
great! good job
ok. I have a few more problems I need you to help me with. Is that ok?
this is one Solve for x: |x + 2| + 16 = 14 x = -32 and x = -4 x = -4 and x = 0 x = 0 and x = 28 No solution
subtract 16 from both sides this gives us |x+2| = -2 since the number on the right side of the equation is negative, there is no solution (there is no value of x we can use to make the left side negative as well)
so the answer is no solution?
this is another problem Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions. Equation 1 Equation 2 |5x - 6| = -41 |7x + 13| = 27 1) Equation 1 has more solutions than equation 2. 2) Equation 1 and Equation 2 have the same number of solutions. 3) Equation 2 has more solutions than Equation 1. 4) The number of solutions cannot be determined.
|5x-6| = -41 has no solutions, because the number on the right is negative |7x + 13| = 27 has two solutions we can find them by solving (7x+13) = 27 and (7x+13) = -27 for x
Is it x=2 and x=-5.71
yes so, we know that Equation 1 has no solutions and Equation 2 has two solutions
so the answer is number 3 right?
ok I have 2 more problems
Solve for x: -3|x + 7| = -12 x = 5/3 , x = - 19/3 x = -3, x = -11 x = -3, x = 11 No solution
divide both sides by -3 then write out the two equations
what would the equations be when you divide both sides by -3? can you do that part for me?
-3|x + 7| = -12 |x+7| = -12/(-3)
now what do I do with those equations?
|x+7| = 4 write out the two equations and solve for x (x+7) = 4 (x+7) = -4
is the answer x=-3 and x=-11
last problem: The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below: 2|x - 6| + 14 = 38 What are the minimum and maximum temperatures for this day? x = -9, x = 21 x = -6, x = 18 x = 6, x = -18 No solution
subtract 14 from both sides then divide both sides by 2 then write the two equations
can you divide both sides by 2 for me. I can't do that.
2|x-6| = 24 divide the left side by 2 divide the right side by 2
would it be (x-3)=12
not quite, remember that the expression inside the absolute value stays the same |x-6| = 12
now write out the two equations like we've done before and solve
is the answer x=18 and x=-6
yup! good job!
ok. Thank you! you were a ton of help! I cant't thank you enough!