Question 1113087
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If {{{abs(7-3x)=10}}} then either {{{7-3x=10}}} or {{{7-3x=-10}}}<br>
Solve each equation separately to find the two solutions.<br>
That is basic algebra, so I leave it to you to finish the problem by this method.<br>
It is often useful to interpret the absolute value equation {{{abs(x-a)=b}}} as meaning that b is the distance between x and a.<br>
For example, {{{abs(x-3)=5}}} means the distance between x and 3 is 5.  So to find the two solutions you go a distance 5 either direction on a number line starting from 3; the two solutions are 3+5=8 and 3-5=-2.<br>
To use this method on your problem, we need to put the equation in the form {{{abs(x-a)=b}}}:
{{{abs(7-3x)=10}}}
{{{abs(3x-7)=10}}}
{{{abs(x-7/3)=10/3}}}<br>
So the two solutions are the numbers that are a distance 10/3 away from 7/3:
{{{7/3+10/3 = 17/3}}}  and  {{{7/3-10/3 = -3/3 = -1}}}.<br>
Those of course are the answers you should get if you finish solving the problem by the method described at the beginning of my response.