- Reasoning D eterm ine w h e th e r each statem en t is always, sometimes, or never t r u e.
a. An eq u a tio n of th e form ax + 1 = ax has no solution.
b. An eq u a tio n in one variable has at least one solution.
c. An e q u a tio n of th e form f = f h as infinitely m any solutions.
Challenge Open-Ended Write an equation with a variable on both sides such that you get
each solution.- x = 5
- No values o fx are solutions.
51. x = 0
54. x is a negative num ber.
52. x can be any number.
55. x is a fraction. - S uppose you have th ree consecutive integers. The greatest of th e th ree integers is
twice as great as the sum of th e first two. W hat are th e integers?
St a n d a r d i ze d Test Pr ep
^AT/ACT 57. W hat is th e solution of - 2 ( 3 x — 4) = — 2x + 2?
CD —| CD | C D 24- Two tim es a n u m b e r plus three equals one half of th e n u m b e r plus 12. W hat is
th e num ber?
CD 3.6 C D 6 CED (^8) CD 10
- Josie’s goal is to ru n 30 m i each week. This w eek she has
already ru n the distances show n in the table. She w ants to
have one day of rest an d to spread out th e rem aining m iles
evenly over th e rest of th e week. W hich eq u a tio n can she
use to find how m any m iles m p er day she m u st run?
CD 4 + 4.5 + 3.5 + 3m = 30 CD 30 - (4 + 4.5 + 3.5) = m
CD 4 + 4.5 + 3.5 + 4m = 30 CD 4 + 4.5 + 3.5 + m = 30
Miles per Day
M Tr• n
w T.....f—
F s s
4 4.5 3.5 I M \
■m;m «Mixed Review
Solve each equation. ^ See Lesson 2-3.- -2a + 5a - 4 = 11 61.6=-3(x + 4) 62. 3(c + |) = 4
- A carp en ter is filling in an open entrancew ay w ith a d oor a n d two side p an els of See Lesson 2-2.
the sam e w idth. The entrancew ay is 3 m wide. The door will be 1.2 m wide. How
wide should the ca rp en ter m ake the panels on eith er side of th e door so th at the
two panels a n d th e door will fill th e entrancew ay exactly?
Get Ready! To p re p a re fo r Lesson 2 - 5 , d o Exercises 6 4 - 6 6.
Evaluate each expression for the given values of the variables. ^9 See Lesson 1 -2.- n + 2m; m = 12, n = -2 65. 3b + c; b = 12, c = 4 66. xy2; x = 2.8, y = 2
108 Ch ap t er 2 So l vi n g Eq u at i o n s