Question

PLEASE HELP ME ANSWER

Write an expression on the line to form an equation on the line to from an equation that has no solution, one solution, or infinitely many solutions.

A. No solution: 2(h + 3) = ___

B. One solution: 2h + 5____

C. 2h - 12 = ____

Answer 1

An equation with no solution is one that leads to a contradiction, an equation with one solution has only one specific value that satisfies it, and an equation with infinitely many solutions occurs when both sides are identical.

Step-by-step explanation:

To write expressions that have either no solution, one solution, or infinitely many solutions, we need to understand that:

• An equation with no solution is one where no value of the variable will make the equation true. Essentially, it leads to a contradiction, such as 2(h + 3) = 2h + 6 + 1, which simplifies to 0 = 1.
• An equation with one solution is an equation where only one specific value for the variable will make the equation true. For example, 2h + 5 = 9 would yield one solution because only h = 2 satisfies the equation.
• An equation with infinitely many solutions is one where any value of the variable will satisfy the equation. This happens when both sides of the equation are identical, like 2h - 12 = 2h - 12.

Example Equations:

A. No solution: 2(h + 3) = 2h + 7

B. One solution: 2h + 5 = 9

C. Infinitely many solutions: 2h - 12 = 2h - 12