You are watching: Solving equation by multiplying or dividing

**Main Rule**The main ascendancy we must remember is that as soon as we division or multiply one next of the equation we have to do the same thing to various other side the the equation. We likewise have to make certain that we divide or main point the entire side that the equation and not simply a part of it.

**Simple Example**We"ll take a simple example first:If 2x = 6, what walk x = ?We have the right to tell by simply looking in ~ this the x = 3, however, us can also solve for it. By learning to fix for x, we can then apply this method to more difficult problems wherein we can"t call the answer simply by looking at the equation.Solving for x2x = 6We want to acquire x by itself on one side of the equation. We have the right to do this by dividing 2x by 2 or multiplying by ½.2x (1/2) = 6 (1/2)(2/2) x = 6/2x = 3

**Let"s shot a more challenging problem.**

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This time us will need to include and subtract together well.3x - 6 = 15It"s easiest to carry out the enhancement and subtraction steps an initial with this kind of equation.add 6 come both sides(3x - 6) + 6 = (15) + 6 3x = 21divide both political parties by 3(3x)1/3 = (21)(1/3)x = 7Now us should check our prize by plugging in x = 7 back into the original equation:3x - 6 = 153(7) - 6 = 1521 - 6 = 1515 = 15

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**Another Example problem with 2 Variables**Solve because that x in the following equation:4x + 3y -12 = 24 - y + 2xAdd 12 come both sides(4x + 3y -12) + 12 = (24 - y + 2x) + 12(4x + 3y) = (36 - y + 2x)Subtract 2x from both sides so there is no x ~ above the best side(4x + 3y) - 2x = (36 - y + 2x) - 2x(2x + 3y) = (36 - y)Subtract 3y from both sides so the 2x is alone ~ above one side(2x + 3y) - 3y = (36 - y) - 3y(2x) = (36 - 4y)Divide both sides by 2 so that we acquire x every alone(2x)1/2 = (36 - 4y)1/2x = 18 - 2yNote the we split both 36 and also 4y by 2 top top the right side.Let"s examine our answer utilizing the initial equation:4x + 3y -12 = 24 - y + 2x4(18 - 2y) + 3y -12 = 24 - y + 2(18 - 2y)72 - 8y + 3y - 12 = 24 - y + 36 - 4y60 - 5y = 60 - 5y

**Things to Remember**Always carry out the same operation to both political parties of the equation.When you multiply or divide, you need to multiply and also divide through the whole side the the equation.Try to perform enhancement and subtraction an initial to gain some multiple of x by chin on one side.Always twin check girlfriend answer by plugging it ago into the initial equation.

**More Algebra Subjects**Algebra glossaryExponentsLinear Equations - IntroductionLinear Equations - slope FormsOrder of OperationsRatiosRatios, Fractions, and PercentagesSolving Algebra Equations with enhancement and SubtractionSolving Algebra Equations through Multiplication and also Division

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