Clear[f[x], r[x], u1[x], u2[x], u3[x], u4[x], f[x], 
      g[x]]
f[x_] := 
      If[5 ≤ x < 6, x - 5, 
        If[6 ≤ x <= 7, 7 - x, 0]]
k = ((100*1000)/(1*1))
r[x_] := (1/(1 + k)) f[x]
u1[x_] := 
      If[(x ≥ 0 && (x - t) >= 
              0), (1/2) (f[x + t] + f[x - t]), 
        0]
u2[x_] := 
      If[(x ≥ 0 && (x - t) ≤ 
              0), (1/2) (f[x + t] - f[-x + t]) + r[t - x], 
        0]
u3[x_] := 
      If[(x ≤ 0 && (x + 2  t) ≥ 0), 
        r[t + (x/2)], 0]
g[x_] := u1[x] + u2[x] + u3[x]
Table[
      Plot[g[x], {x, -10, 10}, 
        PlotRange -> {{-10, 10}, {-1, 1}}, 
        PlotStyle -> {RGBColor[1, 0.7, 0], Thickness[0.02]}], {t, 0, 10, 
        0.1}]