cant solve this

Question

solve the equation by graphing.

Check your solution.

−5 + 1/-4 x = 3x + 6

Answer 1

I am presume that the equation is:

-5 - (1/4)x = 3x+6

Add 5 to both sides:

-(1/4)x = 3x + 11

Add (1/4)x to both sides, and subtract 11 from both sides:

-11 = (13/4)x

Multiply both sides by 4:

-44 = 13x

So x = -44/13

Answer 2

I'm going to assume that Doug C's comment is correct, and follow Mark M.'s suggestion to use grouping symbols to clarify that the left side of the equation is -5 + (-1/4) x

To solve using graphing, you can graph the two lines: y=(-1/4)x - 5 and y = 3x + 6. The solution will be the point these lines have in common.

When you graph these lines, for example in desmos (https://www.desmos.com/calculator/uqlsvf6oxb) or another graphing calculator, you can see they intersect at about x = -3.385.

We can check this by substituting this value of x into the original equation.

-5 - (1/4)(-3.385) = 3(-3.385) + 6

-5 - (-0.84625) = -10.155 + 6

-4.154 = -4.155

This indicates our solution of x = -3.385 is very close but not exact due to rounding.

Answer 3

-5 + 1/(-4x) = 3x+6

multiply all terms by -4x to eliminate the fraction

leaving

20x +1 = -12x^2 -24x

12x^2 +44x +1 = 0

use the quadratic formula to get 2 solutions

x = (-11+/-sqr118)/6

= about -0.023, -3.644

use a graphing calculator, such as desmos online or a TI83 handheld calculator

to graph y=12x^2+44x+1

the x intercepts will be

about (-0.023, 0) and (-3.644, 0)

the graph is an upward opening parabola

which intersects the x axis in two points whose x coordinates are the answers you want

and vertex in quadrant 3

line of symmetry x= -11/6 =-1.8333...

vertex = minimum point = (-11/6, f(-11/6))= (-1.8333..., -39.333....)

= about (-1.8, -39.3)

check your solution by plugging in the x values into the original equation

-5+ 1/-4x = 3x+6

-5+1/4(.023) = 3(-.023)+6

5.87= 5.93 close enough given the rounding approximation for .023

-5+1/4(3.644)= 3(-3.644)+6

-4.931=-4.932 close enough

or graph y=-5+1/(-4x) and y=3x+6

and find where the curve and line intersect

the curve is a rectangular hyperbola with 2 branches

the left upper branch intersects the line in two points