Solving Algebraic
Equations
How do I Solve Algebraic Equations?
1. What ever you add, subtract, multiply or divide
to one side of the equation, you have to do the
same to the other side of the equation!
2. Try to isolate the variable to one side of the
equation.
3. Always substitute your answer for the variable to
see if the answer and equation are true!
PROBLEMS:
Solving Algebraic Equations
Are you ready…
3,2,1… here we go!
Solve the Equation:
v – 10 = -9
Answer:
v - 10 +10 = -9+10
v+0=1
v=1
Solve the Equation:
x
― = 2
5
Answer:
x
(5)∙― = (5)∙2
5
1 ∙ x = 5∙2
x = 5∙2
(What do you notice?)
x = 10
Solve the Equation:
-13m = -377
Answer:
m = 29
Solve the Equation:
n + 4.7 = -4.7
Answer:
n = -9.4
Solve the Equation:
5½ + p = 6
Answer:
p=½
Solve the Equation:
x – 3 = -5½
Answer:
x = -2½
Solve the Equation:
9⅓ = ⁵⁄₃ ∙n
Answer:
n = 5⅗
Solve the Equation:
9
―n
10
=
1
-1―
10
Answer:
n = -1²⁄₉
Solve the Equation:
9x = -2x
Answer:
x=0
Word Problems
Solve the word problem:
A number increased by 34 is 134.
Answer:
n + 34 = 134
n = 100
Solve the word problem: Find the number
Seventy-five less than a number is 62.
Answer:
n - 75 = 62
n = 137
Solve the word problem: Find the number
One-half of a number is 9.
Answer:
½(n)= 9
n = 18
Solve the word problem:
Lisa is cooking muffins. The recipe calls
for 7 cups of sugar. She has already put in
2 cups. How many more cups does she
need to put in?
Answer:
2+c=7
c=5
Solve the word problem:
How many packages of diapers can you
buy with $40 if one package cost $8?
Answer:
p(8) = 40
p=5
Solve the Equation:
1 – r = -5
Answer:
r=6
Solve the Equation:
3p – 2 = -29
Answer:
p = -9
Solve the Equation:
r
― +4=5
10
Answer:
r = 10
Solve the Equation:
k-10
= -7
2
Answer:
k = -4
Solve the Equation:
-5+x
= -1
22
Answer:
x = -17
Solve the Equation:
y
― - 5 = -8
-4
Answer:
y = 12
Solve the Equation:
m
― - 4.9 = -7.11
2.8
Answer:
m = -6.188
Solve the Equation:
X 3
4
+ =
2 5
5
Answer:
x=⅖
Solve the Equation:
3
x
2
+
1
13
=
2
23
Answer:
x = ⁸⁄₉
Solve the Equation:
3c+17=8c-38
Answer:
c = 11
Solve the Equation:
2(6w+5)-7(3-4w)=309
Answer:
w=8
Solve the Equation:
X+1 2x-3 x
+
=
12
33
7
Answer:
x=7
Word Problems
Solve the word problem:
331 students went on a field trip. Six buses
were filled and 7 students traveled in cars.
How many students were in each bus?
(assume each bus was equally filled)
Answer:
6b + 7 = 331
b = 54
Solve the word problem:
Carter had $24 to spend on seven pencils.
After buying them he had $10. How much
did each pencil cost?
Answer:
7p + 10 = 24
or
24 – 7p = 10
p = $2
Solve the word problem:
The sum of three consecutive numbers is 72.
What is the smallest of these numbers?
Answer:
x + (x+1) + (x+2) = 72
x = 23
Solve the word problem:
The sum of three consecutive even numbers
is 48. What is the smallest of these
numbers?
Answer:
x + (x+2) + (x+4) = 48
x = 14
Solve the word problem:
The Math Team made some pies to sell at a
basketball game to raise money for the new math
books. The cafeteria contributed four pies to the
sale. Each pie was then cut into five pieces and
sold. There were a total of 60 pieces to sell. How
many pies did the Math Team make?
Answer:
5(p+4)= 60
p=8
Solve the word problem:
When the magic number is increased by 32
and this result is tripled, the final result is
246. What is the magic number?
Answer:
3(n + 32) = 246
n = 50
Solve the word problem:
On a 30-question test, Makenzie earns 5
points for each correct answer and loses
3 points for every incorrect answer. If
she answers all the questions, and her
score was 6, how many did she answer
correctly?
Answer:
5c – 3(30 – c) = 6
c = 12
Solve the word problem:
The difference between the squares of two
consecutive positive integers is 43. What is
the sum of the 2 integers?
Answer:
(x+1)² - (x) ² = 43
x = 21, x+1=22
Sum=21+22=43
Solve the Equation:
5-4m+9=5(3+m)-9m
Answer:
14 ≠ 15
This equation is never true. There is
no solution.
Solve the Equation:
5-3w+6w=14-3(3-w)
Answer:
5 + 3w = 5 + 3w
5=5
This equation is true for all values of w.
Competition
Problems
Solve the word problem:
Bob spent two-thirds of his money, then he
lost two-thirds of the remainder. If he was
left with $18, how much did he have at the
beginning?
Answer:
$162
Solve the word problem:
Find three consecutive odd integers such that
the sum of twice the first, the second, and
three times the third is 152.
Answer:
23, 25, 27
Solve.
1 4
2
  x
5 9
15
Answer
3
x4
Solve
.
2m 1
 2m  12
5
3
Answer:
m=15
Tickets to the county fair are $8 for
an adult and $5 for a child. If you
have a 15% discount card, how
much will 2 adult tickets and 2 child
tickets cost?
Answer
$22.10
Jake bought a one-month membership
to a fitness center for $35. Each time he
goes, he rents a locker for $0.25. If he
spent $40.50 at the fitness center last
month, how many days did he go?
Answer:
22 days
Simplify.
256
3
8
Answer:
8
Solve.
1
1
2m  16  2m  4
9
3
Answer:
m=-7
Find three consecutive integers
such that three times the sum
of the first two integers is the
same as thirteen more than
four times the third integer.
Answer:
9, 10, 11
Solve.
6
x 4
 1296
Answer:
8
Solve.
3
k  5  15
4
Answer:
k = 25
Solving Absolute Value
Equations
Absolute Value (of x)
•
•
•
•
Symbol lxl
The distance x is from 0 on the number line.
Always positive
Ex: l-3l=3
-4
-3
-2
-1
0
1
2
Ex: x = 5
• What are the possible values of x?
x=5
or
x = -5
To solve an absolute value equation:
ax+b = c, where c>0
To solve, set up 2 new equations, then solve
each equation.
ax+b = c or ax+b = -c
** make sure the absolute value is by itself
before you split to solve.
Ex: Solve 6x-3 = 15
6x-3 = 15 or 6x-3 = -15
6x = 18 or 6x = -12
x = 3 or x = -2
* Plug in answers to check your solutions!
Ex: Solve 2x + 7 -3 = 8
Get the abs. value part by itself first!
2x+7 = 11
Now split into 2 parts.
2x+7 = 11 or 2x+7 = -11
2x = 4 or 2x = -18
x = 2 or x = -9
Check the solutions.
Competition
Problems
Find the sum of the solution(s):
|2x – 1| = 3x + 2.
Answer:
-1/5
(Check your solutions!)
(x=-3 does not work!)
Find the sum of the solutions for
3|2x - 7| - 9 = 15
Answer:
7
(Check your solutions!)