To find the input value [tex]\( x \)[/tex] at which [tex]\( f(x) = g(x) \)[/tex], we need to set the given functions equal to each other and solve for [tex]\( x \)[/tex].
Given:
[tex]\[ f(x) = 1.8x - 10 \][/tex]
[tex]\[ g(x) = -4 \][/tex]
Set [tex]\( f(x) \)[/tex] equal to [tex]\( g(x) \)[/tex]:
[tex]\[ 1.8x - 10 = -4 \][/tex]
Now, solve for [tex]\( x \)[/tex]:
1. Add 10 to both sides of the equation to isolate the term containing [tex]\( x \)[/tex]:
[tex]\[ 1.8x - 10 + 10 = -4 + 10 \][/tex]
[tex]\[ 1.8x = 6 \][/tex]
2. Divide both sides by 1.8 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{6}{1.8} \][/tex]
3. Simplify the right-hand side:
[tex]\[ x = \frac{6}{1.8} = 3.333333333333333 \][/tex]
Therefore, the input value at which [tex]\( f(x) = g(x) \)[/tex] is approximately:
[tex]\[ x \approx 3.33 \][/tex]
Among the choices provided, the correct equation to find the input value is:
[tex]\[ 1.8x - 10 = -4 \][/tex]
This corresponds to the correct evaluation of:
[tex]\[ x = \frac{6}{1.8} = 3.33 \][/tex]
