Sure, let's go ahead and solve the equation.
The equation is given as |(10x+1)/(2)|=(9)/(2).
Since this is an absolute value equation, we will create two separate equations, one for the positive case and one for the negative case.
Case 1: (10x + 1)/2 = 9/2
Solving this equation involves four steps.
1. Multiply every term by 2 to get rid of the denominator: 10x + 1 = 9.
2. Subtract 1 from both sides of the equation: 10x = 8.
3. Divide both sides by 10: x = 0.8.
So, one solution is x = 0.8.
Case 2: -(10x + 1)/2 = 9/2
Solving this equation also involves four steps.
1. Multiply every term by 2 to get rid of the denominator: -(10x + 1) = 9.
2. Distribute the negative sign on the left side: -10x - 1 = 9.
3. Add 1 to both sides of the equation: -10x = 10.
4. Divide both sides by -10: x = -1.
So, the other solution is x = -1.
The solutions of the equation |(10x+1)/(2)|=(9)/(2) are x = 0.8 and x = -1.