Question

select the value for n that guarantees the equation below has infinitely many solutions. 2 (х + 4) = nx +8

Answer 1

To guarantee that the equation has infinitely many solutions, the value of n must be 2.

Step-by-step explanation:

To guarantee that the equation has infinitely many solutions, the value of n must be such that the left side of the equation is equivalent to the right side, regardless of the value of x.

We can solve the equation to find the condition for infinitely many solutions.

Step 1: Distribute 2 to both terms in the parentheses:

• 2(x + 4) = nx + 8
• 2x + 8 = nx + 8

Step 2: Subtract nx from both sides:

• 2x - nx + 8 = 8

Step 3: Factor out x on the left side:

• (2 - n)x + 8 = 8

Step 4: Simplify the equation:

• (2 - n)x = 0

Step 5: Divide both sides by (2 - n):

• x = 0 / (2 - n)

In order to have infinitely many solutions, the denominator (2 - n) must equal 0. This means that n = 2 is the value that guarantees the equation has infinitely many solutions.

Answer 2

The value for n that guarantees the equation 2(x + 4) = nx + 8 has infinitely many solutions is n = 2.

Step-by-step explanation:

To guarantee that the equation 2(x + 4) = nx + 8 has infinitely many solutions, we need to find the value of n that makes both sides of the equation equal.

We can start by solving the equation for x. Distributing the 2, we get 2x + 8 = nx + 8. Subtracting nx and 8 from both sides, we have 2x - nx = 0.

If we factor out x from both terms on the left side, we get (2 - n)x = 0. For the equation to have infinitely many solutions, the expression (2 - n)x must equal zero. Therefore, the value of n that guarantees infinitely many solutions is n = 2.

The complete question is: select the value for n that guarantees the equation below has infinitely many solutions. 2 (х + 4) = nx +8 is: