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Why is it important to keep both sides of the equation equal?
If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.
When you perform the same operations on both sides of the equation the equation stays in what?
The equation remains in 'balance'
How can you solve an equation to get an equivalent equation?
In general, if you apply the same operation to both sides of an equation, you get an equivalent equation - at least if you do simple things like adding, subtracting, multiplying by a non-zero number, and dividing by some number.
What should be added to both sides of this equation 18 plus m27?
Without an equality sign it is not an equation but if you mean 18+m = 27 then by deducting 18 from both sides of the equation m = 9
How do you eliminate fractions in an equation?
Multiply both sides ofthe equation by the 'denominator' of the fraction.
Why is it important to keep both sides of the equation equal?
If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.
Can you divide both sides of the equation by a negative number?
Yes, you can divide both sides of an equation by a negative number, but it is important to remember that this action will reverse the inequality if the equation involves one. For example, if you have an inequality like ( x > y ) and you divide both sides by a negative number, the inequality changes to ( x < y ). In the case of an equation, however, the equality remains valid.
What can be added to both sides of a linear equation?
Equal quantities may be added to both sides of a linear equation.
In general when solving a radical equation you should first the radical and then square both sides.?
In general, when solving a radical equation, you should first isolate the radical on one side of the equation. Once the radical is isolated, you can then square both sides of the equation to eliminate the radical. After squaring, it’s important to check for extraneous solutions, as squaring both sides can introduce solutions that do not satisfy the original equation.
Why do you subtract 6 from both sides?
In any equation, regardless of the number adding or subtracting, multiplying or dividing, you must do the same to both sides. This ensures you are not changing the equation. If only one side was done, then the original equation has been altered and is no longer the same as it began. Changing both sides with the same values keeps all things equal.
The definition of division property of equality?
I think its a property in which both sides of an equation are equal either by adding, subtracting, multiplication, or division.
What kind of quantities can be added or subtracted from both sides of an equation?
You can add or subtract any quantity on both sides of an equation, without changing the equation's solution set. Just make sure you add or subtract the same thing on both sides.
Why is it not necessary to state a division property of equality?
It follows from the multiplication property of equality. Dividing both sides of an equation by the same number (not by zero, of course) is the same as multiply both sides of the equation by the number's reciprocal. For example, dividing both sides of an equation by 2 is the same as multiplying both sides by 0.5.
The in an equation connects both sides of the equation?
The "equal" sign (=) in an equation connects both sides of the equation, indicating that the expressions on either side have the same value. It denotes that the two sides are equal and balanced, showing the relationship between the quantities involved.
What is Both entire sides of a true equation are divided by the same non-zero value then the resulting equation is also true?
Yes because this keeps both sides of the equation in balance.
How do you tell if a equation is balanced?
An equation is balanced when the number of atoms of each element is equal on both sides of the equation. This means that the total mass and charge is conserved. You can check if an equation is balanced by counting the number of atoms of each element on both sides of the equation and adjusting coefficients as needed.
Can both sides of an equation be multiplied by the same?
Yes, both sides of an equation can be multiplied by the same non-zero number without changing the equality. This property is based on the principle that if two expressions are equal, multiplying both by the same value maintains that equality. However, it's important to avoid multiplying by zero, as this would invalidate the equation.
