Question

justify why 16x+8=8(2x+1) has one solution, infinitely many solutions, or no solution

Answer 1

To determine the number of solutions for the equation 16x + 8 = 8(2x + 1), we need to simplify the equation and analyze the resulting expressions.

Step 1: Distribute the 8 on the right side of the equation:
16x + 8 = 16x + 8

Step 2: Rearrange the equation to group similar terms:
16x - 16x = 8 - 8

Step 3: Simplify the equation further:
0 = 0

The outcome indicates that both sides of the equation are equal to zero, which means the equation is always true regardless of the value of x.

Therefore, this equation has infinitely many solutions because any value of x will satisfy the equation.