5 Times the numerator of the solution to 7|8-3h|=21h-49
To find 5 times the numerator of the solution to the equation 7|8-3h|=21h-49, we need to follow these steps:
Step 1: Solve the equation.
Step 2: Find the numerator of the solution.
Step 3: Multiply it by 5.
Let's go through each step in detail:
Step 1: Solve the equation.
Start by isolating the absolute value expression. Divide both sides of the equation by 7 to get rid of the coefficient:
|8 - 3h| = 3h - 7
Next, we need to consider two cases since the absolute value can lead to two possible solutions depending on whether the expression inside it is positive or negative.
Case 1: (8 - 3h) is positive (8 - 3h > 0)
In this case, we can write the equation without the absolute value:
8 - 3h = 3h - 7
Add 3h to both sides and add 7 to both sides to isolate h:
8 + 7 = 3h + 3h
15 = 6h
Divide both sides by 6:
15/6 = h
h = 2.5
Case 2: (8 - 3h) is negative (8 - 3h < 0)
In this case, the equation becomes:
-(8 - 3h) = 3h - 7
Distribute the negative sign inside the parentheses:
-8 + 3h = 3h - 7
Subtract 3h from both sides and add 8 to both sides to isolate h:
-8 + 8 = 3h - 3h
0 = -7
There is no solution for this case.
So, the solution to the equation is h = 2.5.
Step 2: Find the numerator of the solution.
The numerator of a number can be found by converting it into a fraction with 1 as the denominator.
For the solution h = 2.5, we can rewrite it as a fraction:
2.5 = 2.5/1
The numerator of the solution is 2.5.
Step 3: Multiply the numerator by 5.
To get 5 times the numerator, multiply it by 5:
5 × 2.5 = 12.5
So, 5 times the numerator of the solution to the equation 7|8-3h|=21h-49 is 12.5.