Solving Equations and Inequalities
1. Find the solution sets of the following equations.
a)
b)
"
#
(𝑥 + 5) +
#
$
(𝑥 − 2) = 1
"."$%&".'
(
=
".(&".")%
$
2. Find the solution sets of the following inequalities and graph the solution set on the number line.
a) 5𝑥 > 2𝑥 + 9
b)
%&"
#
+
#%'"
$
(%
≤ )
1
3. If the line (𝟐𝒎 + 𝟏)𝒙 + (𝒎 − 𝟑)𝒚 = 𝟓 is passing through the point 𝑨(−𝟏, 𝟑) find the value of 𝑚.
(Hint: If 𝐴 is a point on the line, then 𝑥 and 𝑦 coordinates of the point should satisfy the equation.)
4. a) Draw the graphs of each line
𝒍𝟏 : − 2𝑥 + 𝑦 = 1
𝒍𝟐 : 𝑥 = 2
𝒍𝟑 : 𝑦 = 1
b) Find the area of the triangular region enclosed by these lines.
5. Find the solution set of each system algebraically.
a)
#%' $, - (
(% & #, - $
b)
, - $%
.%'#, - '"
2