if u is between t and b find the value of x and the measure of tu
tu=1-x ub=4x+17 tb=-3
tb = tu+ub
-3 = 1-x + 4x+17
Now just find x, and then tu.
not sure how you get negative lengths.
To find the value of x, we can use the fact that u is between t and b. Since u is between t and b, it means that the point u lies between the points t and b on a number line. Therefore, we can set up an inequality to represent this relationship:
t < u < b
Now let's substitute the given values:
-3 < u < 4x + 17
We also have the equation tu = 1 - x. We can use this equation in conjunction with the inequality to solve for x and find the measure of tu.
Let's start by solving the equation tu = 1 - x for x:
tu = 1 - x
Since we know that tu = 1 - x, we can substitute u with its inequality expression:
1 - x < u < 4x + 17
Now we have two inequalities that tell us the relationship between x and u:
-3 < u < 4x + 17
1 - x < u
Let's combine these inequalities to find the range of values for x:
1 - x < u < 4x + 17 (From the second inequality)
-3 < u < 4x + 17 (From the first inequality)
-3 < u < 4x + 17 < 1 (Combine the two inequalities)
Now let's break this down into two separate inequalities:
-3 < 4x + 17 (1)
4x + 17 < 1 (2)
Solving inequality (1):
-3 < 4x + 17
Subtracting 17 from both sides:
-3 - 17 < 4x + 17 - 17
-20 < 4x
Dividing by 4:
-5 < x
Solving inequality (2):
4x + 17 < 1
Subtracting 17 from both sides:
4x < 1 - 17
4x < -16
Dividing by 4:
x < -4
Combining the results from both inequalities, we have:
-5 < x < -4
Therefore, the value of x is between -5 and -4.
To find the measure of tu, we can substitute x back into the equation tu = 1 - x:
tu = 1 - x
tu = 1 - (-4) (Substituting -4 for x)
tu = 1 + 4
tu = 5
Therefore, the measure of tu is 5 units.