Answer:
x > -7
Explanations:
For the graph g(x), select two points on the line
(-7, 4) and (-2, 8)
That is, x₁ = -7, y₁ = 4, x₂ = -2, y₂ = 8
The slope of the line is given as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{8-4}{-2-(-7)} \\ m\text{ = }\frac{4}{5} \end{gathered}[/tex]
The equation of a line is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{4}{5}(x-(-7)) \\ y\text{ - 4 = }\frac{4}{5}(x+7) \\ y-4=\frac{4}{5}x+\frac{28}{5} \\ y\text{ = }\frac{4}{5}x+\frac{28}{5}+4 \\ y\text{ = }\frac{4}{5}x\text{ + }\frac{48}{5} \\ y\text{ = }0.8x+9.6 \\ g(x)\text{ = 0.8x+9.6} \end{gathered}[/tex]
For the graph f(x):
Select the points (-7, 4) and (-3, 2)
[tex]\begin{gathered} m\text{ = }\frac{2-4}{-3-(-7)} \\ m\text{ = }\frac{-2}{4} \\ m\text{ = -0.5} \end{gathered}[/tex]
The equation of the line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = -0.5(x - (-7)} \\ y\text{ - 4 = -0.5(x + 7)} \\ y\text{ - 4 = -0.5x - }3.5 \\ y\text{ = -0.5x - 3.5 + 4} \\ y\text{ = -0.5x + 0.5} \\ f(x)\text{ = -0.5x + 0.5} \end{gathered}[/tex]
f(x) < g(x)
-0.5x + 0.5 < 0.8x + 9.6
-0.5x - 0.8x < 9.6 - 0.5
-1.3x < 9.1
-x < 9.1 / 1.3
-x < 7
x > -7
