1.2: Linear and Rational Equations
Warm Up:
Find a common denominator to simplify the expressions.
1.
2.
3.
5
6
2
𝑥
+
3
+
3
1
−
𝑥−4
8
4
4
𝑥+3
https://www.fairviewhs.org/staff/jack-cawelti/classes/advancedalgebra-2/calendar/2016/9
Linear Equations
Solve each linear equation
Don’t forget to check your answers!
1. 3𝑥 − (2𝑥 − 2) = 4(𝑥 + 4)
2. 4𝑦 − 3(1 − 𝑦) = 7𝑦 + 5
3. 4(𝑛 + 2) + 3 = 7𝑛 − (3𝑛 − 11)
 An identity is an equation that is satisfied by every number.
 A conditional equation is an equation that is satisfied by at least
one number, but is not an identity.
 An inconsistent equation is an equation with no solution.
o We say its solution is ∅, the empty set
4.
𝑥+3
2
𝑥
+ =2
6
A rational equation is an equation containing one or more rational
expressions.
Solve the rational equations.
5.
2
𝑥−1
3
4
𝑥
𝑥
+ =
Is there anything we should be careful of in that last problem?
6. Find any restrictions on the variable, then solve:
a.
4
𝑥+5
+
2
𝑥−5
=
20
𝑥 2 −25
b.
1
𝑥−4
−
6
𝑥+2
=
12
𝑥 2 −2𝑥−8
Get out your graphing calculators!
7. Solve:
𝑥−1
3
+2=
3𝑥+2
2