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Solve |x–1| = 6x + 12

Sagot :

Answer:

[tex]x = - \frac{11}{7} [/tex]

Step-by-step explanation:

1) Break down the problem into these 2 equations.

[tex]x - 1 = 6x + 12[/tex]

[tex] - (x - 1) = 6x + 12[/tex]

2) Solve the first equation. x - 1 = 6x + 12

[tex]x = - \frac{13}{5} [/tex]

3) Solve the second equation: -( x - 1 ) = 6x + 12.

[tex]x = - \frac{11}{7} [/tex]

4) Collect all solution.

[tex]x = - \frac{13}{5}. - \frac{11}{7} [/tex]

5) Check solution.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.We will drop x=-\frac{13}{5}x=−513 from the solution set.

6) Simplify.

[tex]x = - \frac{11}{7} [/tex]

Therefor, the answer is x = - 11/7.

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