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Practice
Linear(Simple) Equations
Easy
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Linear(Simple) Equations: Very Difficult Problems with Solutions
Problem 1
A number is equal to 7 times itself minus 18. Which is the number?
Solution:
The statement is equivalent to the following equation:
[tex]x=7x-18[/tex]
[tex]18=7x-x[/tex]
[tex]6x=18[/tex]
[tex]x=3[/tex]
Problem 2
A number is equal to 4 times this number less 75. What is the number?
Solution:
Let us denote the number with n. The problem can be rewritten as
n=4n-75
. By substracting
n
from both sides, we get
3n-75=0
. Now we divide both sides by 3 to get
n-25=0
, or
n=25
.
Problem 3
Two times a number, decreased by 12 equals three times the number, decreased by 15. Which is the number?
Solution:
Let us denote the number with n. We rewrite the problem as
2n-12=3n-15
. We substract
2n
from both sides and get
-12=n-15
. Then we add 15 to both sides in order to get
n=3
.
Problem 4
Twice a number equals 5 times the same number plus 18. Which is the number?
Solution:
[tex]2x=5x+18[/tex]
[tex]3x=-18[/tex]
[tex]x=-6[/tex]
Problem 5
If
a + b= 29 , b + c = 45, a + c = 44
Find
a + b + c = ?
Solution:
(a + b) + (b + c) + (a + c) = 29 + 45 + 44
a + b + b + c + a + c = 118
2a + 2b + 2c = 118
2(a + b + c) = 118
a + b + c = 59
Problem 6
Solve the equation: [tex](11x - 5)^2 - (10x - 1)^2 - (3x - 20)(7x + 10) = 124[/tex]
Solution:
Answer: x = -5
Problem 7
[tex]x- \frac{1-\frac{3x}{2}}{4} = \frac{2-\frac{x}{4}}{3} - \frac{11}{12}[/tex]
Solution:
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