Reversing operationsThe goal in fixing an equation is to obtain the change by chin on one next of the equation and a number top top the various other side the the equation.
To isolation the variable, we must reverse the operations acting on the variable. We do this by performing the station of each operation on both sides of the equation. Performing the same operation on both sides of an equation walk not readjust the validity of the equation, or the worth of the variable the satisfies it.
Reversing multiple Operations
When an ext than one operation acts on a variable in an algebraic equation, apply the turning back of the order of operations to reverse the operations. Here is the stimulate in i m sorry you should reverse operations:Reverse addition and individually (by subtracting and also adding) exterior parentheses. Reverse multiplication and division (by dividing and multiplying) external parentheses. Eliminate (outermost) parentheses, and also reverse the to work in order follow to these three steps. Be certain to examine your answer! The worth of the variable, when plugged in for the variable, should make the equation true.
Example 1: settle for x: 5x + 9 = 44Reverse addition: 5x + 9 - 9 = 44 - 95x = 35Reverse multiplication:
Example 2: deal with for y: 3( - 1) = 15No addition or subtraction outside the parenthesesReverse multiplication: 3( -1)÷3 = 15÷3( - 1) = 5Within parentheses:Reverse subtraction: - 1 + 1 = 5 + 1 = 6Reverse division: ×4 = 6×4y = 24No parentheses. Check: 3(
Example 3: settle for z: 4(3(z - 11) + 6) = 48No addition or subtraction. Reverse multiplication:
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Check: 4(3(13 - 11) + 6) = 48 Thus, z = 13.