Question

les ago. Mathematics • High School Which of the following has infinitely many solutions? A)5x-10=x+20 B)2(6+x)=14+2x C)10x+5=3(5x+7) D)2(4+x)=8+2x

Answer 1

D) 2(4+x)=8+2x​

Step-by-step explanation:

To be able to determine which of the equations has infinitely many solutions, let's go ahead and solve for x in each of the equations. The equation with infinitely many solutions will have zero on both sides.

1. 5x - 10 = x + 20, to solve for x;

`\begin{gathered} 5x+x=20+10 \\ 6x=30 \\ x=(30)/(6)=5 \end{gathered}`

From the solution, x = 5, we can see that this isn't the right option.

2. 2(6+x)=14+2x, let's solve for x;

`\begin{gathered} 12+2x=14+2x \\ 2x-2x=14-12 \\ 0=2 \end{gathered}`

This too isn't the correct option.

3. 10x+5=3(5x+7)

To solve for x;

`\begin{gathered} 10x+5=15x+21 \\ 10x-15x=21-5 \\ -5x=16 \\ x=(16)/(-5)=-3.2 \end{gathered}`

This isn't the correct option too.

4. 2(4+x)=8+2x​

Let's solve for x;

`\begin{gathered} 8+2x=8+2x \\ 2x-2x=8-8 \\ 0=0 \end{gathered}`

We see from the solution that this is the equation with infinitely many solutions.