Answer:
To find the solutions to the equation f(x) = g(x), we need to set the two functions equal to each other and solve for x.
Setting f(x) = g(x), we have:
−0.2x − 3 + 2.3x − 2 + 7x − 10.3 = −|0.2x| + 4.1
Combining like terms, we get:
8.1x - 15.3 = -|0.2x| + 4.1
Next, we'll consider two cases for the absolute value term.
Case 1: 0.2x ≥ 0
In this case, the absolute value can be removed, and the equation becomes:
8.1x - 15.3 = -0.2x + 4.1
Combining like terms again:
8.3x - 15.3 = 4.1
Adding 15.3 to both sides:
8.3x = 19.4
Dividing both sides by 8.3:
x ≈ 2.34 (rounded to the nearest hundredth)
Case 2: 0.2x < 0
In this case, we need to change the sign of the absolute value term and solve separately:
8.1x - 15.3 = 0.2x + 4.1
Combining like terms:
7.9x - 15.3 = 4.1
Adding 15.3 to both sides:
7.9x = 19.4
Dividing both sides by 7.9:
x ≈ 2.46 (rounded to the nearest hundredth)
Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 2.34 and x ≈ 2.46.