David W. answered • 12/05/15
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Hi,
Sorry, but this is not a linear equation. It is an algebraic equation with a variable m that has some value -- we can easily solve for the value m. The equation will produce a single value of m, not a line for which every point [often with coordinates (x,y) would make the equation true].
Let's find the value of (m).
The same operation (addition, subtraction, multiplication, division, etc.) may be done to equal values and the results will be equal.
So, we could subtract 10 from both sides of the equation 3m+10=16 to get:
3m = 6
Those values are also equal.
Then, we could divide both sides of the equation by 3 to get:
m = 2
Those values are also equal (and that means that 3*2+10=16). We found the value of m. It is not a line; it is a single value.
The process works like this: If the expression in the problem has addition, then we subtract. If it has subtraction, then we add. If it has multiplication, then we divide. If it has ... [get the idea?] Isolate the variable (here it is m) on one side of the equals and the answer appears on the other side.
David W.
THX, Doug. We're still working on updating text books to make that a Constant Declaration (like computer software does -- since the value of the 'variable' does not vary; you know, like Pi or e does not vary).
Linear Equation: The general form of Linear Equations are ax + b = 0, where a is not equal to 0.
Solution of a Linear Equation: The value of the variable which when substituted for the variable in the equation, makes its two sides equal, is called a solution (or root) of the equation.
How to solve Linear Equations in one variable:
Rules for solving linear equations:
The equality of a linear equation is not changed,
Rule 1 : When the same number is added to both sides of the equation.
Rule 2: When the same number is subtracted from both sides of the equation.
Rule 3 : When both sides of the equation are multiplied by the same non-zero numbers.
Rule 4: When both sides of the equation are divided by the same non-zero number.
Solution of a Linear Equation: The value of the variable which when substituted for the variable in the equation, makes its two sides equal, is called a solution (or root) of the equation.
How to solve Linear Equations in one variable:
Rules for solving linear equations:
The equality of a linear equation is not changed,
Rule 1 : When the same number is added to both sides of the equation.
Rule 2: When the same number is subtracted from both sides of the equation.
Rule 3 : When both sides of the equation are multiplied by the same non-zero numbers.
Rule 4: When both sides of the equation are divided by the same non-zero number.
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12/05/15
David W.
Oh, I feel guilty that I might mislead a serious student or a really gullible tutor. That first line was meant to be humor.
As quoted (from linearequations.org) in the previous comment, ax+b=0 is a linear equation in one variable.
Food for thought, though: If x+2=4 is a linear equation in one variable, then is x=2 a solution or is it another linear equation in one variable?
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12/05/15
Doug C.
12/05/15