# Solving equations with variables on both sides with fractions on one side

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4. Check whether the unknown variable is on one side or both sides of the equation. We can move one term from one side of the equality to the other by changing the sign of each term that is moved in the process. The procedure is called transposing. 5. Transpose the terms with the unknown variable to one side of the equality and
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"Change Sides Change Signs" is a short-cut in showing work. If we move a term from one side of the equation (right side of the equal sign) to the other side (left side of the equal sign), then the value of the term has an opposite value.
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We can do this by subtracting. 2. 2 2 from both sides of the equation since doing the same operation on both sides of the equation ensures that both sides are still equal: A + 2 − 2 = B − 2, which is equivalent to A = B − 2. A + 2 - 2 = B - 2,\ \text { which is equivalent to }\ A = B - 2.
Solving Equations with Variables on Both Sides (03:19) Example #2: 3 5 − x + 12 = 4 –12 –12 *Subtraction Property (Subtract 12 from both sides of the equation.) 3 5 − x = –8 . 5 3 − (3 5 − x) = –8(5 3 − ) *Multiplication Property (multiply both sides of the equation by (–5/3), the reciprocal of –3/5.) 1 x = 40 3. x = 40 3 ... Solution: Let first multiple of 8 = 8a. Therefore, second consecutive multiple of 8 = 8 ( a + 1) And, third consecutive multiple of 8 = 8 ( a + 2 ) Since, sum of three consecutive multiples of 8 = 888 as given in the question. Therefore, 8a + [8 (a + 1)] + [8 (a + 2)] = 888. ⇒ 8a + (8a + 8) + (8a + 16) = 888. When solving a simple equation, think of the equation as a balance, with the equals sign (=) being the fulcrum or center. Thus, if you do something to one side of the equation, you must do the same thing to the other side. Doing the same thing to both sides of the equation (say, adding 3 to each side) keeps the equation balanced.
The variable is the letter on the left-hand side (LHS) of the equation. The variable is multiplied by two. I want the x to stand alone on one side of the equation. Since the x is multiplied by 2, I need to divide on both sides by 2, in order to get the variable by itself.
As shown in the video, this method simply involves performing basic equation manipulations so that the variable terms are segregated to one side of the equation and the constant terms remain on the other. Solving the equation now simply requires dividing the entire equation by the coefficient of the variable to get the required answer.
Students learn that if a fraction appears in an equation, the first step is to get rid of the fraction by multiplying both sides of the equation by the denominator of the fraction. If two or more terms in an equation are fractions with the same denominator, the first step is to get rid of the fractions by multiplying both sides of the equation ... Variables on Both Sides WRITE: Some problems produce equations that have variables on both sides of the equal sign. Solving an equation with variables on both sides is similar to solving an equation with a variable on only one side. You can add or subtract a term containing a variable on both sides of an equation. Solve Equations with Variables on Both Sides. What if there are variables on both sides of the equation? For equations like this, begin as we did above—choose a “variable” side and a “constant” side, and then use the subtraction and addition properties of equality to collect all variables on one side and all constants on the other side.
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