To find the input value [tex]\(x\)[/tex] at which [tex]\(f(x) = g(x)\)[/tex], we need to set the functions [tex]\(f(x) = 1.8x - 10\)[/tex] and [tex]\(g(x) = -4\)[/tex] equal to each other and solve for [tex]\(x\)[/tex].
The equation we need to solve is:
[tex]\[ 1.8x - 10 = -4 \][/tex]
Now, let's solve this equation step-by-step to find the value of [tex]\(x\)[/tex].
1. Add 10 to both sides:
[tex]\[ 1.8x - 10 + 10 = -4 + 10 \][/tex]
This simplifies to:
[tex]\[ 1.8x = 6 \][/tex]
2. Divide both sides by 1.8:
[tex]\[ x = \frac{6}{1.8} \][/tex]
Thus, the value of [tex]\(x\)[/tex] where [tex]\(f(x) = g(x)\)[/tex] is:
[tex]\[ x = 3.\overline{3} \][/tex]
Therefore, the correct equation and solution are:
[tex]\[ 1.8x - 10 = -4 \quad ; \quad x = \frac{10}{3} \][/tex]
So, the input value [tex]\(x\)[/tex] where [tex]\(f(x) = g(x)\)[/tex] is:
[tex]\[ x = \frac{10}{3} \approx 3.333\overline{3} \][/tex]
Hence, the correct option is:
[tex]\[ 1.8x - 10 = -4 ; x = \frac{10}{3} \][/tex]
