Question

First do distributive property on the left side and then Combine like terms on the right side and then determine if there will be one solution, no solution or infinitely many solutions.7(2x – 1) = 1 - 8 + 14x.

A. One solution
B. No solution
C. Infinitely many solutions

Answer 1

After applying the distributive property and combining like terms, the equation simplifies to both sides being the same, leading to the statement 0 = 0, which is always true. Thus, the equation has infinitely many solutions.

Step-by-step explanation:

First, let's apply the distributive property to the left side of the equation 7(2x – 1). This gives us 14x - 7. Now, let's combine like terms on the right side of the equation 1 - 8 + 14x, which simplifies to -7 + 14x. So now we have 14x - 7 = -7 + 14x.

Next, if we try to isolate x on one side, we quickly realize that both sides of the equation have the same terms, 14x - 7. So, if we subtract 14x and add 7 to both sides, all terms cancel out, leaving us with a statement of 0 = 0, which is always true. Therefore, we have infinitely many solutions because any value of x will satisfy this equation.