Question

Draw lines to match each equation on the left to its number of solutions on the right.​

Answer 1

1) The equation
`2(4x-1)=-8x-2` has one solution

2) The equation
`2(4x-1)=8x-2` has infinitely many solutions

3) The equation
`-2(4x-1)=-8x-2` has no solution.

Explanation:

We need to solve the equation and match with its solution.

1)
`2(4x-1)=-8x-2`

Solving and finding value of x:

`2(4x-1)=-8x-2\\8x-2=-8x-2\\8x+8x=-2+2\\16x=0\\x=0`

So, We get x =0

So, the equation
`2(4x-1)=-8x-2` has one solution

2)
`2(4x-1)=8x-2`

Solving the equation and finding value of x:

`2(4x-1)=8x-2\\8x-2=8x-2\\8x-8x=-2+2\\0=0`

So, We get 0 =0

So, the equation
`2(4x-1)=8x-2` has infinitely many solutions

3)
`-2(4x-1)=-8x-2`

Solving the equation and finding value of x

`-2(4x-1)=-8x-1\\-8x+2=-8x-2\\-8x+8x=-2-2\\0\\eq -4`

So, we get 0 ≠ -4

So, the equation
`-2(4x-1)=-8x-2` has no solution.