Vocabulary
Each of the letters without an unknown value
Unknown
The square root of a number plus six is equal to fifteen
x – (2x + 2) = –3
x–2x–2=–3 → x=1
Calculate the number that when added to two is equal to ten.
x+2=10 → x=8
Solve equation:
4x – 2x = 2x + 10 – 2x
x = 5
Formed by two algebraic expressions separated by and equal sign (=)
Algebraic equality
A number cubed minus that same number squared is equal to eighteen.
x3 - x2 = 18
Find the solution:
6x – (1 – x) = 4x – 4
6x–1+x=4x–4 → 6x+x–4x=–4+1 → x=–1
Which values of x make the equality x(x – 1) = x2 + 1 true?
a) x = –2
b) x = 0
c) x = 3
d) x = –4
e) x = 2
f) x = –1
f) x = -1
Solve solution
–x + 5 = 2x – 10
x = 5
Two equations are equivalent when they have the same ______.
Solutions
The square of the difference between a number and a third of that same number is equal to thirty six.
(x - x/3)2 = 36
Find the solution
9x – (8 + x + 12) = –x + 7
9x–8–x–12=–x+7 → 9x–x+x=7+8+12 → x=3
In a class there are twice as many girls as boys. If there is a total of 30 students, how many girls and boys are there in the class?
x+2x = 30 → x=30/3 → x=10
There are 10 boys and 20 girls
Solve equation
2x – 15 = 3x + 4
x = -19
If we ___or______ the same number or algebraic expression to both members of an equation, we obtain an equivalent equation
Add or subtract
The sum of a number and its consecutive number is equal to eleven
x + 3(x - 1) + 4 = 8 - x
x+3x–3+4=8–x → x+3x+x=8+3–4 → x=7/5
The sum of two numbers is 55. One of the numbers is a quarter of the other one.
Calculate both numbers.
x + x/4 = 55 → x = 220/5 → x = 44
The numbers are 44 and 11
The difference between a number and that number minus 1 then halved is equal to 13.
x = 25