Algebraic Word Problem#2 - Need Help Please

Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2x and y = 4x−2 intersect are the solutions of the equation 2x = 4x−2. (4 points)

Part B: Make tables to find the solution to 2x = 4x−2. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 2x = 4x−2 graphically? (2 points)

Answer 1

(A)

 

Let

 

y₁(x) = 2x

y₂(x) = 4x - 2

 

At the intersection of the two lines,

 

y₁(x) = y₂(x).

 

Therefore,

 

2x = 4x - 2

 

(B)

 

2x = 4x - 2

 

Solve for x and get

 

2 = 2x

 

x = 1

 

There is no table of x values, because there is exactly one value of x that satisfies the equation 2x = 4x - 2.

 

(C)

 

Draw the lines on a properly scaled and labeled Cartesian grid, and note the x-coordinate of the point where the lines intersect.  The line for y = 2x goes through the origin and (1,2).  The line for y = 4x - 2 goes through (0,-2) and (1,2).  Draw the lines through these respective points, and note their intersection at (1,2). 

 

Answer 2

Part A)

 

The x value makes the two y values the same.

 

 

Part B)

 

x      |        2x       |          4x - 2

____________________________

-4              -8                    -18

-3              -6                    -14

-2              -4                    -10

-1              -2                      -6

0                0                       -2

1                2                        2

2                4                        6

3                6                       10

4                8                       14

 

The solution is x=1.  This x value makes both y values equal to 2.

 

 

Part C)

 

2x = 4x - 2

 

Subtract 4x on both sides of equation.

 

-2x = -2

 

   x = 1