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When the variable is on both sides of the equation it is perfectly acceptable to solve each side by itself?
Wiki User
∙ 13y ago
You have to have the variable ending on at most one side of the equal sign. If you end up with no variables, you will have either an infinate solution(Ex. 5=5) or no solution (Ex. 6=14)
Also... Each side needs equal treatment.
EX: 15a+3b=45c
divide all parts by an LCD [3]
15a/3=5a
3b/3=b
45c/3=15c
Thus
5a+b=15c
This is as far as it goes...
Wiki User
∙ 13y ago
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Is the goal in solving an equation to get the variable by itself?
Yes
To use inverse operations on both sides of an equation until the variable appears by itself on one side?
Isolate the variable
What is a two-step equation?
A two Step equation is simply an equation that requires two steps to solve it.Example3h + 4 = 16 *Get the Variable by itself- when doing that know thataddition and Subtraction always come before Multiplicationand subtraction. - 4 = - 43h = 123h / 3 = 12 / 3h = 12 / 3 => h = 4
How do you get the variable by its self if its in a fraction?
if you have a variable in a fraction and want it by itself you have to rearrange the equation e.g. 2x/1=1 to get the variable by itself you first need to get rid of the fraction SO... you multiply both sides by the denominator (in this case it's 1) so you end up with 2x=1 to get the variable alone you then need to get rid of the coefficient, which in this case is 2. To get rid of this coefficient you need to divide both sides by two (because the variable is multiplied by 2) so then you end up with 2x/2=1/2 We can then simplify to x=1/2.
Is a variable with no power assumed to be to the power of one?
Yes. If we don't see an exponent, the exponent is understood to be one. Just like if we don't see a sign, the sign is assumed to be positive. This in no way constricts or limits the variable. The variable can still be anything at all. But assumptions like this are part of mathematics. How tedious would it be to have to write "x1" for each x? In any case, x1 = x so it is almost pointless.Yes, because if the variable (hypothetically speaking) is 1 (and it can be any number in the world, but 1 is an example), and the exponent (power) is 1, there is only one number to multiply, therefore, the number can only be by itself. If it is squared (to the second power) then you multiply the variable against itself (in this case, 1 X 1), but if the variable doesn't have an exponent, it is assumed to be to the power of one. Take the number 2, for example. If 2 is the variable, x, and x is alone, and you multiply how big the number is of the exponent, and because there is none, it is to the first power.X squared looks like this: x X xX (a.k.a. x to the first power) looks like this: xIf there is no exponent, you only multiply what is there, which there is only one variable, so it is assumed to be to the first power. If it were squared, or to the second power as demonstrated above, you would multiply x by itself. If you count the variables in the equation, x squared has two x's, while x alone has only one x in the equation. Because there is only one x, and the exponent represents how many of that number (in this case, x) you multiply by itself, x is assumed to be to the first power, or to the power of one.
Is the goal in solving an equation to get the variable by itself?
Yes
Which would be the independent variable and which would be the dependent variable?
A dependent variable is usually on the side of the equation by itself. The independent variable usually has something being done to it. And, the dependent variable is usually written to the left of the equation.
Is the goal of solving an equation to get the variable by itself?
No. The goal is to find a value of the variable(s) for which the solution is true. Getting the variable by itself is only a part of the process, not the goal.
To use inverse operations on both sides of an equation until the variable appears by itself on one side?
Isolate the variable
What does it mean to solve a formula for a variable that appears on both sides?
It means that you manipulate the equation in such a way that the variable appears only on one side, by itself.
What does it mean when the result of solving a linear equation is x equals 0?
Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.
When solving an equation how can you tell the variable is by itself?
there is nothing being added or multiplied to it, and it is on its own side of the equal sign
Tariq said you can write an equation by setting an expression equal to itselfWould an equation like this be trueexplain?
Yes. Any number, or expression, is equal to itself. An equation such as:x + 5 = x + 5 is true for ANY value of "x".
What is the first step in solving a 2step equatioin?
Add the inverse to both sides of the equation to get the variable term by itself. ex: 3x + 7 = -8 Add -7 to both sides of the equation this 'cancels' the +7 on the left leaving 3x, the variable term, alone on the left.
Is x-7 equal to -3?
-4
What does isolate mean in math?
To completely isolate the variable, we have to divide both sides of the equation by 6. x = 24 / 6 x = 4 Now, x is all by itself or "isolated". We can read the answer right from the equation. x equals 4. To review, isolating the variable means getting every term containing the variable on one side of the equationfound on google...
What does it mean to isolate the variable?
Let's say you are given a complex equation involving two variables, x and y, and say you are asked to solve for x, but x is located on both sides of the equals sign. Using various algebraic techniques, you will have to manipulate the equation so that the x is by itself on one side of the equation and everything else is on the other side. That is called isolating the variable.
