U moet uitvind watter x { displaystyle x}
equals if you have a problem like 7x−10=3x+6{displaystyle 7x-10=3x+6}
. This kind of equation is called a linear equation, and it usually has just one variable. This article will walk you through the simple steps.
Steps
Method 1 of 2: Starting with the Variables on Opposite Sides
Stap 1. Kyk na u probleem
'N Eenvoudige lineêre vergelyking kan soos 7x − 10 = 3x − 6 { displaystyle 7x-10 = 3x-6} lyk
Stap 2. Gaan die vergelyking na vir verskillende terme en konstante terme
Wisselende terme is getalle soos 7x { displaystyle 7x}
3x{displaystyle 3x}
6y{displaystyle 6y}
or 10z{displaystyle 10z}
where the number changes depending on what you plug into the variable, or letter. Constant terms are numbers like 10{displaystyle 10}
6{displaystyle 6}
or 30{displaystyle 30}
where the number never changes.
Usually, equations won't come with varying terms and constant terms lined up on separate sides. In the example above, the left-hand side (LHS) has both varying and constant terms, as does the right-hand side (RHS)
Stap 3. Berei die getalle voor sodat die verskillende terme aan die een kant en die konstante terme aan die kant is, soos in 16x − 5x = 32−10 { displaystyle 16x-5x = 32-10}
(that equation is solved in example 2).
In order to do this, you may have to subtract or add the numbers you want to move from both sides. In the next step, you'll see how to do that in example 1.
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The equation 16x−5x=32−10{displaystyle 16x-5x=32-10}
does have all the varying terms on one side (LHS), while all the constant terms are on the other side (RHS).
Stap 4. Skuif die verskillende terme na die een kant van die vergelyking
Dit maak nie saak na watter kant jy die verskillende terme skuif nie.
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In voorbeeld 1, 7x − 10 = 3x − 6 { displaystyle 7x-10 = 3x-6}
can be rearranged by choosing to subtract either 7x{displaystyle 7x}
or 3x{displaystyle 3x}
from both sides. Choosing to subtract 7x{displaystyle 7x}
you have:
(7x−7x)−10=(3x−7x)−6−10=−4x−6{displaystyle {begin{aligned}(7x-7x)-10&=(3x-7x)-6\\-10&=-4x-6\end{aligned}}}
Stap 5. Bring al die konstante terme na die ander kant van die vergelyking
Dit is: skuif die konstante terme sodat hulle aan die teenoorgestelde kant van die vergelyking is van waar die verskillende terme is.
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Ons sien dat −6 { displaystyle -6}
must be subtracted from both sides:
−10−(−6)=−4x−6−(−6)−4=−4x{displaystyle {begin{aligned}-10-(-6)&=-4x-6-(-6)\\-4&=-4x\end{aligned}}}
Stap 6. Verdeel beide kante deur die koëffisiënt van x { displaystyle x}
The coefficient of x{displaystyle x}
(or y{displaystyle y}
or z{displaystyle z}
or any letter) is the number in front of the varying term.
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The coefficient of x{displaystyle x}
in −4x{displaystyle -4x}
is −4{displaystyle -4}
. So divide both sides by −4{displaystyle -4}
to get the value of x=1{displaystyle x=1}
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Our answer to the equation 7x−10=3x−6{displaystyle 7x-10=3x-6}
is x=1{displaystyle x=1}
. You can check this answer by plugging 1{displaystyle 1}
back into every x{displaystyle x}
variable and seeing if both sides of the equation equal the same number:
7(1)−10=3(1)−6−3=−3{displaystyle {begin{aligned}7(1)-10&=3(1)-6\\-3&=-3\end{aligned}}}
Method 2 of 2: Starting with the Variables on One Side
Step 1. Know that sometimes the varying terms and the constant terms will be separate
Sometimes, half of your work will be done for you. You'll have all the varying terms on one side and all the constant terms on the other side. If this is the case, all you have to do is the following.
Stap 2. Vereenvoudig albei kante
Vir die vergelyking 16x − 5x = 32−10 { displaystyle 16x-5x = 32-10}
we just have to subtract the numbers from one another.
Stap 3. Verdeel dan beide kante deur die koëffisiënt van x { displaystyle x}
remember that the coefficient of x is the number in front of the varying term.
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in this example, the coefficient of x{displaystyle x}
in 11x{displaystyle 11x}
is 11{displaystyle 11}
. that division is 11x/11=22/11{displaystyle 11x/11=22/11}
to get x=2{displaystyle x=2}
. the answer to the equation 16x−5x=32−10{displaystyle 16x-5x=32-10}
is x=2{displaystyle x=2}
warnings
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why do it that way? trying to divide this: 4x−10=−6{displaystyle 4x-10=-6}
like this 4x/4−10/4=−6/4{displaystyle 4x/4-10/4=-6/4}
creates x−10/4=−6/4{displaystyle x-10/4=-6/4}
with a lot of fractions to handle, and that's not so easily solved; so, simplifying is one good reason to get all the variable terms onto one side and all the constant terms onto the other side.
