Download Hybrid Elementary Algebra 2.1 – 2.3 Introduction Solving Equations

Hybrid Elementary Algebra
2.1 – 2.3 Introduction
Solving Equations: Solving an equation means find the number or numbers to substitute in for the
variable that result in a true statement.
Addition Principle: You can add the same quantity to both sides of an equation.
Multiplication Principle: You can multiply both sides of an equation by the same nonzero quantity.
Solve each equation.
2. x − 8 = 5
1. y + 7 = −4
y + 7 − 7 = −4 − 7
____________________
y = −11
____________________
3. 3 x = 18
4.
3 x 18
=
3
3
____________________
x=6
____________________
5.
2
t −1 = 5
3
⎛2
⎞
3 ⎜ t − 1⎟ = 3 ( 5 )
⎝3
⎠
4
y =8
5
6. 5 x − 9 = 21
____________________
⎛2 ⎞
3 ⎜ t ⎟ − 3 (1) = 3 ( 5 ) ____________________
⎝3 ⎠
2t − 3 = 15
____________________
2t = 18
____________________
t =9
____________________
Hybrid Elementary Algebra
2.1 – 2.3 Introduction
Page 2 of 3
7. 7 r − ( 2r + 8 ) = 32 + r
7r − 2r − 8 = 32 + r
____________________
7 r − 2r − r = 32 + 8
____________________
4r = 40
____________________
r = 10
____________________
9.
3
−15
( 2 x + 5) =
2
2
3x +
15 −15
=
2
2
____________________
15 ⎞
⎛
⎛ −15 ⎞
2 ⎜ 3x + ⎟ = 2 ⎜
⎟ ____________________
2⎠
⎝
⎝ 2 ⎠
6 x + 15 = −15
____________________
6 x = −30
____________________
x = −5
____________________
8.
2
2
+ 4t = 6t −
3
15
10.
1
( 2 x − 1) = 7
3
Hybrid Elementary Algebra
2.1 – 2.3 Introduction
Page 3 of 3
Solve each equation for the indicated variable.
11. d = rt for t .
d rt
=
r r
____________________
d
=t
r
____________________
13. P = 2l + 2w for w .
P − 2l = 2w
____________________
P − 2l
=w
2
____________________
12. f =
n
for n .
15
14. Q =
a+b
for a .
2
OR
P
−l = w
2
____________________
15. A = rx + sx for x .
A = x (r + s)
____________________
A
=x
r+s
____________________
16. A = P + Prt for P .