How do you solve the absolute value $| 3 x - 1 | + 10 = 25$ $abs(3x-1) + 10 = 25$ ?

Question

How do you solve the absolute value $| 3 x - 1 | + 10 = 25$ $abs(3x-1) + 10 = 25$ ?

1 Answer

Impact of this question

2023 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-13T12:10:17

Actually there are two conditions to look at:

(1) If $3 x - 1 \geq 0$ $3x-1>=0$ we have:

$(3 x - 1) + 10 = 25 \to 3 x = 25 + 1 - 10 = 16 \to$ $(3x-1)+10=25->3x=25+1-10=16->$
$x = 16 / 3 = 5 \frac{1}{3}$ $x=16//3=5 1/3$

(2) If $3 x - 1 < 0$ $3x-1<0$ the absolutes 'turn it around':

$- (3 x - 1) + 10 = 25 \to - 3 x = 25 - 1 - 10 = 14 \to$ $-(3x-1)+10=25->-3x=25-1-10=14->$
$x = 14 / (- 3) = - 4 \frac{2}{3}$ $x=14//(-3)=-4 2/3$

Validation:
(allways do this, sometimes one of the answers is wrong)
(1) exists if $x \geq \frac{1}{3}$ $x>=1/3$ which is consistent with the answer
(2) exists if $x < \frac{1}{3}$ $x<1/3$ which is also consistent with the answer

Final answer: $x = 5 \frac{1}{3} or x = - 4 \frac{2}{3}$ $x=5 1/3orx=-4 2/3$

Science

Math

Humanities

... and beyond

How do you solve the absolute value $| 3 x - 1 | + 10 = 25$ $abs(3x-1) + 10 = 25$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the absolute value abs(3x-1) + 10 = 25|3x−1|+10=25abs(3x-1) + 10 = 25?

1 Answer

Related questions

Impact of this question

How do you solve the absolute value $| 3 x - 1 | + 10 = 25$ $abs(3x-1) + 10 = 25$ ?