Writing Equations
Lania has 8 times more pens as Janiyah.
l = 3j.
9x-8
Linear, exponent on the variable x is 1.
Is -4 the solution to 3x+4 = -8?
Yes -8 = -8.
Variable.
A symbol that represents an unknown value (usually represented by a letter).
The difference of a number and 8 is 56.
x-8=56
45x2+6x-7x
Non-Linear, highest exponent on variable is 2.
Is −𝟓 a solution to the equation 𝟔𝒙 + 𝟓 = 𝟓𝒙 + 𝟖 + 𝟐𝒙? Explain
No, because -25 ≠ -27.
Inverse Operation.
Opposite Operation. (Ex. Opposite of addition is subtraction.)
The reciprocal of a number and 9 is 42.
9/x = 42.
The quotient of x and 5.
x/5, Linear.
Is −3 a solution to the equation 3𝑥 − 5 = 4+ 2𝑥? Explain.
No, -14 ≠ -2.
Coefficient
The number in front of the variable (Ex. In -3x, -3 is the coefficient.)
The sum of three consecutive integers is 45.
x+x+1+x+2 = 45.
The reciprocal of a number and 8.
8/x, non linear, 8/x can be rewritten as 8x-1, so the exponent on x is -1.
Write an equation that has the solution x = 6.
Example solutions: 6x = 36, 6+x = 12, x-4 = 2 etc.
Term
Number or variable parts of expression separated by + or - sign.
The sum of four consecutive odd integers is −96.
x+x+2+x+4+x+6 = -96
The cube of a positive number divided by the square of the same positive number
x3/x2 (not linear) but if simplified, x3/x2 = x, so the simplified form is linear.
Check each solution to see if they satisfy the linear equation -4(v+3) = -12-4v? Explain.
1. v = 2,
2. v = -1
3. v = 0
Yes, because -4(v+3) and -12-4v are equivalent expressions.
Like Terms
Terms with same variable and exponent. (For example, 8x2 and -5x2 are like terms because they have the same variable and exponent. Constants such as 8 and 5 are also considered like terms because we can combine them together.)