How to solve |5x-6|=3?

Question

Kaylee Rhodes · Accepted Answer

We must pay extra attention to this issue because it involves the absolute value function.
A negative or positive integer can be changed into a positive number using the absolute value function.
Thus, we need to solve the term inside the absolute value for both the positive and negative value it is equated to, in this case +3 and -3.
Solution 1)

5 x - 6 = 3

5 x - 6 + 6 = 3 + 6

5 x - 0 = 9

5 x = 9

\frac{5 x}{5} = \frac{9}{5}

\frac{5 x}{5} = \frac{9}{5}

x = \frac{9}{5}

Solution 2)

5 x - 6 = - 3

5 x - 6 + 6 = - 3 + 6

5 x - 0 = 3

5 x = 3

\frac{5 x}{5} = \frac{3}{5}

\frac{5 x}{5} = \frac{3}{5}

x = \frac{3}{5}

Jayla Gross · Accepted Answer

We know:                                       |      5      x      -      6      |        =    3  So in effect we have:            |      ±      3      |        =    +    3  So everything inside the | | must end up as positive or negative 3.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~                              Set                           5        x        -        6        =        -        3            Increase both sides by 6      5    x    =    +    3  Split each side by 5                    x        =        +                  3          5                    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~                              Set                           5        x        -        6        =        +        3            Increase both sides by 6      5    x    =    +    9  Split each side by 5                    x        =        +                  9          5                    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~                              Putting it all together                                |      5      x      -      6      |        =    +    3        x    =          3      5                      and                x    =          9      5       are solutions

How to solve |5x-6|=3?

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