Question

Communicate precisely: How is solving 2x+c=d similar to solving 2x + 1 = 9 for x? How are they different? How can you use 2x+c=d to solve 2x + 1 = 9? (© MP.6)

Answer 1

Solving 2x + c = d is similar to solving 2x + 1 = 9 because both involve linear equations that require isolating x to find its value. Though the specific values of c and d differ, the technique of subtracting c and dividing by the coefficient of x applies to both. Checking the solution for reasonableness is a critical final step.

Step-by-step explanation:

Solving the equation 2x + c = d is similar to solving 2x + 1 = 9 because both are linear equations that can be solved for x by using similar techniques. To solve either equation, you perform the following steps:

1. Identify the unknowns and knowns in the equation.
2. Isolate the variable x by performing inverse operations to cancel out other terms. For the equation 2x + c = d, you would subtract c from both sides. For 2x + 1 = 9, you would subtract 1 from both sides.
3. Divide both sides by the coefficient of x (which is 2 in these examples) to solve for x.

In the equation 2x + c = d, c and d are constants or known values but are left as letters. In 2x + 1 = 9, c is specifically 1 and d is 9.

You can apply the method used for 2x + c = d directly to solve 2x + 1 = 9. For the given equation, subtract 1 from both sides to get 2x = 8 and then divide by 2 to find x = 4.

Lastly, check your answer to ensure it's reasonable by substituting it back into the original equation to see if it holds true.

Answer 2

Solving 2x + c = d is similar to solving 2x + 1 = 9 because both involve linear equations that require isolating x to find its value. Though the specific values of c and d differ, the technique of subtracting c and dividing by the coefficient of x applies to both. Checking the solution for reasonableness is a critical final step.

Step-by-step explanation:

Solving the equation 2x + c = d is similar to solving 2x + 1 = 9 because both are linear equations that can be solved for x by using similar techniques. To solve either equation, you perform the following steps:

1. Identify the unknowns and knowns in the equation.
2. Isolate the variable x by performing inverse operations to cancel out other terms. For the equation 2x + c = d, you would subtract c from both sides. For 2x + 1 = 9, you would subtract 1 from both sides.
3. Divide both sides by the coefficient of x (which is 2 in these examples) to solve for x.

In the equation 2x + c = d, c and d are constants or known values but are left as letters. In 2x + 1 = 9, c is specifically 1 and d is 9.

You can apply the method used for 2x + c = d directly to solve 2x + 1 = 9. For the given equation, subtract 1 from both sides to get 2x = 8 and then divide by 2 to find x = 4.

Lastly, check your answer to ensure it's reasonable by substituting it back into the original equation to see if it holds true.

Answer 3

Solving 2x + c = d is similar to solving 2x + 1 = 9 because both involve linear equations that require isolating x to find its value. Though the specific values of c and d differ, the technique of subtracting c and dividing by the coefficient of x applies to both. Checking the solution for reasonableness is a critical final step.

Step-by-step explanation:

Solving the equation 2x + c = d is similar to solving 2x + 1 = 9 because both are linear equations that can be solved for x by using similar techniques. To solve either equation, you perform the following steps:

1. Identify the unknowns and knowns in the equation.
2. Isolate the variable x by performing inverse operations to cancel out other terms. For the equation 2x + c = d, you would subtract c from both sides. For 2x + 1 = 9, you would subtract 1 from both sides.
3. Divide both sides by the coefficient of x (which is 2 in these examples) to solve for x.

In the equation 2x + c = d, c and d are constants or known values but are left as letters. In 2x + 1 = 9, c is specifically 1 and d is 9.

You can apply the method used for 2x + c = d directly to solve 2x + 1 = 9. For the given equation, subtract 1 from both sides to get 2x = 8 and then divide by 2 to find x = 4.

Lastly, check your answer to ensure it's reasonable by substituting it back into the original equation to see if it holds true.