Leonard ran 4 miles more than Sheldon ran. The sum of their distances is 26 miles. How far did Sheldon run? The domain

a. Define your variable.
b. Write algebraic expressions for the distances each person ran.
c. Write an equation that can help you solve the problem.
d. Solve the equation by using the supplied set of possible solutions.
e. Check your answer.
of the solution is {0, 4, 11, 22}.

a. X = Sheldon's distance.

x+4 = Leonard's distance.

c. x + x+4 = 26.

d. 2x = 26-4 = 22.
X = 11.

a. Define your variable:

Let x be the distance Sheldon ran (in miles).

b. Write algebraic expressions for the distances each person ran:
Since Leonard ran 4 miles more than Sheldon, the distance Leonard ran can be expressed as (x + 4) miles.

c. Write an equation that can help you solve the problem:
The sum of their distances is 26 miles. So, the equation becomes:
x + (x + 4) = 26

d. Solve the equation by using the supplied set of possible solutions:
Let's substitute each value from the solution set {0, 4, 11, 22} into the equation and check which values satisfy the equation:

When x = 0:
0 + (0 + 4) = 4, which is not equal to 26

When x = 4:
4 + (4 + 4) = 12, which is not equal to 26

When x = 11:
11 + (11 + 4) = 26, which is equal to 26
So, x = 11 satisfies the equation.

Therefore, Sheldon ran 11 miles.

e. Check your answer:
To check if Sheldon ran 11 miles, we add his distance to Leonard's distance and verify if it gives us the total distance of 26 miles:
11 + (11 + 4) = 11 + 15 = 26
Since the sum is indeed 26, our answer is correct.