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WILL GIVE BRAINLIEST! HELP!

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.

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

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

Respuesta :

Answer:


Part A: The graphs intersect whenever both have the same (x,y) values.

G1 = {(x,y) such that y = 2x}

G2 = {(x,y) such that y = 4x - 2}

G1 ∩ G2 = {(x,y) such that

(x = x) & (y = 2x) & (y = 4x - 2)}

= {(x,y) such that (y = 2x) & (2x = 4x - 2)}


Part B: equation solves to x = 1, but

x = -4, -8 = -16 - 2, false.

x = -3, -6 = -12 - 2, false.

x = -2, -4 = -8 - 2, false.

x = -1, -2 = -4 - 2 = -6, false.

x = 0, 0 = -2, false.

x = 1, 2 = 4 - 2, true.

x = 2, .... do I gotta do the rest???


Part C, solve graphically by drawing straight lines on graph paper, first through (-4,-8) and (4,8), and second through (-4,-14) and (4,14).

They intersect at (1,2).


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