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17x=-85 x=-5 how did i get this answer

I know x=-5 but how did i get that answer

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Kathryn D. | Worry-Free, Stress-Free, Katie D. You can count on me.Worry-Free, Stress-Free, Katie D. You ca...
4.9 4.9 (274 lesson ratings) (274)

When you're solving an equation for a variable (in this case x) you are trying to get x on one side of the equal sign all by itself. To do that, you do the opposite of what is being done to it (so that you can get the number in front of the x to equal 1). So when you have:

17 x = -85 

x is multiplied by 17 -- to get rid of that 17, we have to divide by 17 on both sides of the equation. You have to do it on both sides of the equation to keep the equation balanced.  

17 x ÷ 17 = -85 ÷ 17

On the left side of the equation the 17s get canceled out (specifically because 17/17 = 1), so what you're left with is:

x = -85 ÷ 17

That you can punch into a calculator to get 

x = -5


Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (363 lesson ratings) (363)

Remember, if you do the same thing to both sides of a true equation, you get a true equation. In this case we can divide both sides by 17:

17x/17 = -85/17

x = -5


Garland R. | Teacher By Day / Tutor By NightTeacher By Day / Tutor By Night

One last addition to both of these perfect answers:  Dividing both sides of the equation by 17 is referred to as the "inverse operation" of the equation's current multiplication of 17x.