Solve the equation |4x+5|=|−29+4x|. Graph the solutions, if possible.
the graph line i was given cant go past/below -10 and 10...and because of this i cant figure this out T-T....
|4x+5|=|−29+4x|
4x + 5 = -29 + 4x OR 4x+5 = 29 - 4x
5 = -29 <--- no solution, or null set
or
8x = 24
x = 3
check:
LS = |4x+5| = |17| = 17
RS = |-29 + 12| = |-17| = 17
so x = 3 , which lies between -10 and +10 of your number line
thx u so much! i had it right then, i just thought i was doing the 5=-29 wrong
To solve the equation |4x+5|=|−29+4x|, we need to consider two cases:
Case 1: (4x + 5) = (−29 + 4x)
Simplifying this equation, we get:
4x + 5 = -29 + 4x
Notice that the 4x term cancels out on both sides of the equation. This means that both sides are equal, regardless of the value of x. Therefore, this equation has infinitely many solutions.
Case 2: -(4x + 5) = (−29 + 4x)
Simplifying this equation, we get:
-4x - 5 = -29 + 4x
Adding 4x to both sides, we get:
-5 = -29 + 8x
Adding 29 to both sides, we get:
24 = 8x
Dividing both sides by 8, we get:
x = 3
Therefore, the solution to the equation |4x+5|=|−29+4x| is x = 3.
Now, let's graph the solution x = 3 on the given graph line that cannot go past/below -10 and 10. Since the solution is x = 3, we plot a point at (3, 0) on the graph.
However, if the graph line cannot go past/below -10 and 10, and the solution is x = 3, then the point (3, 0) would not be within the allowed range. Therefore, the solution cannot be represented on the given graph.
To solve the equation |4x+5|=|−29+4x|, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: (4x+5) is positive, so we don't need to take the absolute value.
In this case, we have 4x + 5 = -29 + 4x. By subtracting 4x from both sides, we get 5 = -29, which is not true. Therefore, there are no solutions for this case.
Case 2: (4x+5) is negative, so we need to take the absolute value.
In this case, we have -(4x + 5) = -(-29 + 4x). Simplifying this equation, we get -4x - 5 = 29 - 4x. By adding 4x and 5 to both sides, we get 0 = 34. This is also not true. Therefore, there are no solutions for this case either.
Since there are no solutions for either case, the equation |4x+5|=|−29+4x| has no solutions.
As for graphing the solutions, since there are no solutions, the graph would be empty, indicating that there are no points on the graph that satisfy the equation.