Question

How is solving +=2 x plus c equals d similar to solving +=2 x plus 1 equals 9 for x? How are they different? How can you use +=2 x plus c equals d to solve +=2 x plus 1 equals 9?

Answer 1

Let's break down your questions step by step.

1. Solving +=2x + c = d: In this equation, you have an expression +=2x + c on the left side equal to d on the right side. This equation contains variables x, c, and d.
2. Solving +=2x + 1 = 9 for x: In this equation, you have an expression +=2x + 1 on the left side equal to 9 on the right side. This equation also contains variable x.

Now, let's compare the two equations:

Similarities:

• Both equations involve solving for the variable x.
• Both equations contain the expression +=2x on the left side.

Differences:

• The first equation, +=2x + c = d, introduces additional variables c and d, making it more general and requiring knowledge of the values of c and d to find a specific solution.
• The second equation, +=2x + 1 = 9, is a specific case where c is 1 and d is 9. You already have specific values for c and d.

To use the first equation +=2x + c = d to solve the second equation +=2x + 1 = 9, you would need to equate the two equations, recognizing that c is 1 and d is 9 in the second equation:

+=2x + c = d

+=2x + 1 = 9

Now, you can substitute the values of c and d from the second equation into the first equation:

+=2x + 1 = 9

Now, you have a simplified equation that is similar to the second equation, and you can proceed to solve for x:

+=2x + 1 = 9

Subtract 1 from both sides:

+=2x = 9 - 1

+=2x = 8

Divide both sides by 2 to isolate x:

x = 8 / 2

x = 4

So, by recognizing the values of c and d in the second equation and substituting them into the first equation, you arrive at the same solution for x, which is x = 4.