Question

for 2 and 3, find x.
2.
a b c
5 2x + 6
x + 10
3.
a b c
9x + 7 - 3x + 20
39
for questions 4 and 5, u is between t and b. find the following.

1. tu = 2x, ub = 3x + 1, tb = 21
2. tu = 4x - 1, ub = 2x - 1, tb = 5x

x = ____
tu = ____
ub = ____
tb = ____
x = ____
tu = ____
ub = ____
tb = ____

Explanation:

Step1: Set up equation for 2

$5+(2x + 6)=x + 10$

Step2: Simplify left - hand side

$2x+11=x + 10$

Step3: Solve for x

$2x-x=10 - 11$, $x=-1$

Step4: Set up equation for 3

$(9x + 7)+(-3x + 20)=39$

Step5: Combine like terms

$6x+27 = 39$

Step6: Solve for x

$6x=39 - 27$, $6x=12$, $x = 2$

Step7: Set up equation for 4

$2x+(3x + 1)=21$

Step8: Combine like terms

$5x+1 = 21$

Step9: Solve for x

$5x=20$, $x = 4$
$TU=2x=8$, $UB=3x + 1=13$, $TB = 21$

Step10: Set up equation for 5

$(4x-1)+(2x - 1)=5x$

Step11: Combine like terms

$6x-2 = 5x$

Step12: Solve for x

$6x-5x=2$, $x = 2$
$TU=4x-1=7$, $UB=2x - 1=3$, $TB=5x = 10$

Answer:

1. $x=-1$
2. $x = 2$
3. $x = 4$, $TU=8$, $UB=13$, $TB = 21$
4. $x = 2$, $TU=7$, $UB=3$, $TB = 10$