Making Sure these are right?
absolute value:
1.|7x+2|=10
x=1.1 x=1.7
2.|3x-5|=-1
x=1.3 x=2
1. Eliminate the absoulute value :
7 x + 2 = 10
7 x + 2 = - 10
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7 x + 2 = 10
7 x = 10 - 2 = 8
x = 8 / 7
7 x + 2 = - 10
7 x = - 10 - 2 = - 12
x = - 12 / 7
Solutions x = 8 / 7 aprox. 1.14 and x = - 12 / 7 aprox. - 1.71
2.Eliminate the absoulute value :
Absolute value can't be negative.
No solutions exist.
So if the absolute vale equals a negative number there is no solution?
Such as:
|x^2+2x+1|=-4
So, that has no solution?
To solve absolute value equations, you need to isolate the absolute value expression on one side of the equation and then consider both the positive and negative solutions.
1. |7x + 2| = 10:
Drop the absolute value signs and create two separate equations, one with the expression inside the absolute value bars as positive and one with it as negative.
For the positive case: 7x + 2 = 10
Solve for x: 7x = 8 --> x = 8/7 ≈ 1.14
For the negative case: -(7x + 2) = 10
Solve for x: -7x - 2 = 10 --> -7x = 12 --> x = -12/7 ≈ -1.71
So, the solutions are x = 1.14 and x = -1.71 (rounded to two decimal places).
2. |3x - 5| = -1:
Notice that the absolute value of a real number is never negative, so there are no solutions for this equation.