To determine the input value [tex]\( x \)[/tex] at which [tex]\( f(x) \)[/tex] equals [tex]\( g(x) \)[/tex], we need to solve the equation [tex]\( f(x) = g(x) \)[/tex].
Given the functions:
[tex]\[ f(x)=1.8x-10 \][/tex]
[tex]\[ g(x)=-4 \][/tex]
To find the input value where these two functions are equal, set [tex]\( f(x) \)[/tex] equal to [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) = g(x) \][/tex]
[tex]\[ 1.8x - 10 = -4 \][/tex]
Now, solve this equation step-by-step:
1. Add 10 to both sides to isolate the term with [tex]\( x \)[/tex] on one side:
[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]
Simplify the fraction:
[tex]\[ x = \frac{6}{1.8} = \frac{60}{18} = \frac{10}{3} \][/tex]
Therefore, the input value [tex]\( x \)[/tex] at which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[ x = \frac{10}{3} \][/tex]
Thus, the correct answer is:
[tex]\[ 1.8x - 10 = -4; x = \frac{10}{3} \][/tex]
