Question

Does 4(2x+1)=5(x+2)+3 have one solution , no solution or many solutions

Answer 1

Given equation is :

• 4 (2x + 1) = 5 (x + 2) + 3

Now, 4 (2x + 1) = 5 (x + 2) + 3 will be equal to

=> 8x + 4 = 5x + 10 + 3

=> 8x - 5x = 10 + 3 - 4

=> 3x = 9

=> x = 9/3

=> x = 3

Hence, on the number line the total solutions for given equation is one which is x = 3.

However, on the Cartesian plane :

The equation will be :

=> x + 0y = 3

Hence, there are infinite values possible y, such as :

• x = 3, y = 5

=> 3 + 0 × 5 = 3

• x = 3, y = 2

=> 3 + 0 × 2 = 3

And many more...

Hence, there are many solutions for the equation on Cartesian plane.