HELP!!!Solving this equation...?

Question

I really need your help!!!

I'm supposed to solve this equation graphically and algebraically...

abs(4x-3) = 5*sqrt(x+4)

[the absolute value of (4x-3) is equal to 5 times the square root of (x+4)]

I'm really lost and have no clue how to go about this problem...and if you could help to describe the graph as well i would be very grateful!!THANKS!

Instructions about each step would help me as well...THANKS SO MUCH!!!

Answer 1

abs(4x-3) = 5*sqrt(x+4) divide both sides by 5

abs(4x-3)/5 = sqrt(x+4) square both sides

abs(4x-3)(4x-3)/5*5 = x+4 do the math on left side

abs(16x^2 -12x - 12x +9/25) = x + 4 multiply both sides by 25

abs(16x^2 - 24x + 9) = 25x + 100 substract 9 form both sides

abs(16x^2 - 24x) = 25x + 91 subtract 25x from each side

abs(16x^2 - 49x) = 91 put it in quadratic form

abs(16x^x - 49x - 91) = 0 solve for x

abs(x =    9.2631) or abs(x =     -6.2006) applys abs

x=9.2631 or  x=6.2006

Your graph would look something like this:

You would have two parabolas on the positive (x,y) quadrant that bottom out at the two values of x. The would go screaming off into infinity.

Answer 2

Square both sides, you willl get

    (4x-3)^2 = 25(x+4)

  => 16x^2 - 24x + 9 = 25x + 100

=> 16x^2 - 49x - 91 = 0

solve this quadratic equation and you will get the answer. Both of these numbers will satisfy the equation.

Answer 3

Note that |4x+3| = 4x + 3 for 4x+3 ≥ 0  and -4x -3 when

4x+3 < 0  .  

That means |4x+3| = 4x + 3 for x ≥ -3/4  and -4x -3 when

x < -3/4 .

Next the the domain of 5√(x+4) is [-4,∞)  so

for [-4,-3/4) we would solve   -4x -3 =5√(x+4)

and for [-3/4,∞) we solve  4x+3 = 5√(x+4)  

Graphing is a great idea at this point because the points

of intercection of the graph give you a great illustration of the solution.  

The square root graph is the top half of a sideways parabola with vertex at (-4,0) and the absolute value graph

is a V with slope of -4 to left of vertex and 4 to right of vertex

and the vertex is at (-3/4,0) .  That V should cross the radical

graph twice, once between -4 and -3/4 and once to the

right of -3/4 .  

   Solve the two algebraic equations for the unknown values

of x  

   Graphically, you will probably use a TI-82,83,83+,84+,84+ silver edition  to plot the graphs, zoom and trace the solutions, or some darn accurate point plotting on graph paper