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Explanation:
The complete question is attached below. In order to solve this problem, we'll use a graphing tool. First of all, we'll say that the LHS is a linear function and the RHS is another linear function, so for each case, we'll have:
[tex]f(x)=g(x)[/tex]
For each graph, [tex]f(x)[/tex] will be drawn in red while [tex]g(x)[/tex] will be drawn in blue.
Case 1:
[tex]f(x)=\frac{1}{4}x+\frac{5}{2}x-2 \\ \\ g(x)=4-\frac{1}{4}x[/tex]
So by equating both equations:
[tex]\frac{1}{4}x+\frac{5}{2}x-2=4-\frac{1}{4}x[/tex]
By using graphing tool we get a point of intersection at which the x-value is the solution to our equation. So:
Solution:
[tex]\boxed{x=2}[/tex]
See First Figure below.
Case 2:
[tex]f(x)=7.9x+x+4 \\ \\ g(x)=-1.1x-16[/tex]
Applying a similar method as in case 1.
Solution:
[tex]\boxed{x=-5.8}[/tex]
See Second Figure below.
Case 3:
[tex]f(x)=3.2x+5.7 \\ \\ g(x)=-2.5x[/tex]
Applying a similar method as in case 1.
Solution:
[tex]\boxed{x=-1}[/tex]
See Third Figure below.
Case 4:
[tex]f(x)=10.1x-1.6x+44 \\ \\ g(x)=-7[/tex]
Applying a similar method as in case 1.
Solution:
[tex]\boxed{x=-6}[/tex]
See Fourth Figure below.
Learn more:
Methods for solving system of equations: https://brainly.com/question/10185505
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