2-4 So l v i n g Eq u a t i o n s W i t h V a r i a b l e s o n Bo t h Si d e s
Quick Review
W hen an equation has variables on b o th sides, you can use
properties of equality to isolate the variable on one side. An
equation has no solution if no value of th e variable m akes
it true. An equation is an identity if every value of the
variable m akes it true.Example
What is the solution of 3x — 7 = 5x + 19?
3x - 7 - 3x = 5x + 19 — 3 x S ubtract 3x.
-7 = 2x + 19 Simplify.
-7 - 19 = 2x + 19 - 19 Subtract 19.
-2 6 = 2x Simplify.
= y Divide each side by 2.
-1 3 = x Simplify.Exercises
Solve each equation. If the equation is an identity, write
identity. If it has no solution, write no sol ut i on.- \x + 4 = §x - 2 25. 6 - 0 .2 5 /= /- 3
- 3 [h - 4) = —^(24 - 6 h) 27. 5 n = 20(4 + 0.25rc)
- Archit ect ur e Two buildings have th e sam e total
height. O ne b uilding has 8 floors w ith height h. The
oth er building has a g round floor of 16 ft an d 6 o th er
floors with height h. W rite a n d solve an eq u a tio n to
find th e height h of these floors. - Travel A train m akes a trip at 65 m i/h. A plane
traveling 130 m i/h m akes th e sam e trip in 3 fewer
hours. W rite a n d solve an eq u a tio n to find the
distance of th e trip.
2-5 Li t er al Eq u at i o n s an d Fo r m u l as
Quick Review
A literal equation is an eq u a tio n th a t involves two or
m ore variables. A formula is an equation th at states a
relationship am ong quantities. You can use properties of
equality to solve a literal equ atio n for one variable in term s
of others.Example
What is the width of a rectangle with area 91 ft 2 and
length 7 ft?
A = (w Write the appropriate formula.
A
j = w Divide each side by €.
qi
-f = w Substitute 91 for A and 7 fo r €.
13 = w Simplify.
The w idth of the rectangle is 13 ft.Solve each equation for x.
30. a x + b x - - c 31.^ j-c+ l = 0- m - 3x = 2x + p 33. p + | = s
Solve each problem. Round to the nearest tenth, if
necessary. Use 3.14 for it.- W hat is th e w idth of a rectangle w ith length 5.5 cm
a n d area 220 cm2? - W hat is th e radius of a circle w ith circum ference
94.2 mm? - A triangle h as height 15 in. an d area 120 in.2. W hat is
the length of its base?
T 5 4 C h a p t e r 2 So l v i n g Eq u a t i o n s