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+10v + 0 = 1

v = 1

Solve the Equation:

― = 2x5

Answer:

(5)∙― = (5)∙2

1 x = ∙ 5 2∙x = 5 2∙

(What do you notice?)

x = 10

x5

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:

―n = -1― 9 1 10 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 = 134n = 100

Solve the word problem: Find the number

Seventy-five less than a number is 62.

Answer:

n - 75 = 62n = 137

Solve the word problem: Find the number

One-half of a number is 9.

Answer:

½(n)= 9n = 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 = 7c = 5

Solve the word problem:

How many packages of diapers can you buy with $40 if one package cost $8?

Answer:

p(8) = 40p = 5

Solve the Equation:

1 – r = -5

Answer:

r = 6

Solve the Equation:

3p – 2 = -29

Answer:

p = -9

Solve the Equation:

― + 4 = 5r10

Answer:

r = 10

Solve the Equation:

= -7k-102

Answer:

k = -4

Solve the Equation:

= -1-5+x22

Answer:

x = -17

Solve the Equation:

― - 5 = -8y-4

Answer:

y = 12

Solve the Equation:

― - 4.9 = -7.11m

2.8

Answer:

m = -6.188

Solve the Equation:

+ = X2

35

45

Answer:

x = ⅖

Solve the Equation:

x + 1 = 2 32

13

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+112

2x-333

x7

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 = 331b = 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 = 24or

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 = 43x = 21, x+1=22

Sum=21+22=43

Solve the Equation:

5-4m+9=5(3+m)-9m

Answer:

14 ≠ 15This equation is never true. There is no solution.

Solve the Equation:

5-3w+6w=14-3(3-w)

Answer:

5 + 3w = 5 + 3w5 = 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

152

94

51 x

Solve.

Answer

4

3-x

122

3

1

5

2 m

m

Solve.

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

8

3

256

Simplify.

Answer:

8

423

1162

9

1 mm

Solve.

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

12966 4 x

Solve.

Answer:

8

1554

3k

Solve.

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 = -156x = 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 = -18x = 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!)