How do you solve for x: #|2x − 9| = 11#?

Question

Kennedy Adams · Accepted Answer

#x=-1#
OR
#x=10# First you can seperate the equation into two possible cases to get rid of the absolute value sign: #1)2x-9=11# #2)2x-9=-11# For case number one, you have to isolate the variable, #x#. TO do that you must get rid of the constant, -9, by adding the additive inverse*, or in our case, 9 on both sides to get #2x=20#. Finally you can get rid of the coefficient, or the 2 in our case, by multiplying the multiplicative inverse**, in our case -2 on both sides to get our variable, #x=10# For case number two, you also need to isolate the variable, #x#. You do the same exact thing as case number one, adding the additive inverse on both sides. In equation 2, the constant is still -9 so you have to add 9, the additive inverse, on both sides to get #2x=-2# Finally, you can multiply the coefficient,2, by the multiplicative inverse, -2 to get the variable by itself.Once you do this you get #x=-1# So, the answers to #|2x-9|=11# are #x=10# and #x=-1# *an additive inverse is the number that, when added to a number #x#, yields zero **a multiplicative inverse is the number that, when multiplied to a number #x# yields 1

Eva Adamson · Answer

undefined To solve for x in the equation |2x - 9| = 11, you first isolate the absolute value expression. Then, you set up two equations: 2x - 9 = 11 and 2x - 9 = -11. Solve each equation separately for x to find the possible values of x.