Download Literal Equations

Literal Equations & Inequalities
Literal: More than one variable
To solve for a variable means to rewrite an equation as an equivalent equation in which the variable is on one
side and does not appear on the other side.
Example: Area of a triangle
1
Solve A  bh for the height. Find the height of a triangle with a base of 4 in and area of 18 in2.
2
2(18)
h
2A  bh
4
2A
h  9 in
h
b
1
Example: Area of a trapezoid - Solve A  (b1  b2 )h for b1 .
2
2 A  (b1  b2 )h
2A
 b1  b2
h
2A
b1 
 b2
h
Example: Solve bx + ux + ch = er for x
x(b  u )  ch  er
*make sure to factor out the x so that there is only one!
x(b  u )  er  ch
er  ch
x
bu
Example: Solve
x
hx
a
for x
m
m
x
hx
m  ma  m
m
m
x  ma  h  x
2x  ma  h
ma  h
x
2
3( x  1) x
 4
5
3
Lowest common denominator is 15
Example: Solve 2 x 
3( x  1) x


15  2 x 
  4
5
3


30 x  9( x  1)  5 x  60
30x  9x  9  5x  60
34x  69
69
x
34
Linear Inequality – can be written in one of the following forms, where a and b are real numbers and a  0 .
ax  b  0
ax  b  0
ax  b  0
ax  b  0
Compound Inequality – consists of two simple inequalities joined by “and” or “or”.
Solution – a value that, when substituted for the variable, results in a true statement.
Graph – all points on a number line that represent solutions.
Solution Set – a range of answers is written in brackets with the lower bound listed first, then a comma, then the
upper bound. We use soft brackets ( ) when the bounds are non-inclusive
(< and >). We use hard
brackets [ ] when the bounds are included (  and  )
Example:
4  2x   ; {reals}
2 x  2
x  1 **Remember to switch the sign when dividing by a negative!
Graph on a number line:
Solution in interval notation: (, 1)
Example:
**always write your solution set from least to greatest
**always use () for 
8(2 x  1)  11x  17 ; {integers}
16x  8  11x 17
16x  11x  9
5x  9
9
x
5
Graph:
*Since the domain is {integers}, only graph dots on the integers
Solution: { -1, 0, 1, …  } **list specific integers in the solution set
Example:
5  2x  3  15 ; {reals}
8  2 x  12
4  x  6
Compound inequality. Break it up.
Graph:
Solution: (-4, 6)
Example:
x  7  4 or 7  x  1 ; {reals}
x  3
x6
Graph:
Solution:
 , 3 6, 
sometimes written  , 3
This is called a “disjunction”
 6, 