To find the input value [tex]\( x \)[/tex] at which [tex]\( f(x) = g(x) \)[/tex], we need to set the equations [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] equal to each other. Given the functions:
[tex]\[ f(x) = 1.8x - 10 \][/tex]
[tex]\[ g(x) = -4 \][/tex]
Set these two equations equal to each other:
[tex]\[ 1.8x - 10 = -4 \][/tex]
Now solve for [tex]\( x \)[/tex]:
Step 1: Add 10 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 1.8x - 10 + 10 = -4 + 10 \][/tex]
[tex]\[ 1.8x = 6 \][/tex]
Step 2: Divide by 1.8 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{6}{1.8} \][/tex]
Simplifying this fraction:
[tex]\[ x = \frac{6}{1.8} = 3.\overline{3} \][/tex]
Therefore, the correct value of [tex]\( x \)[/tex] is:
[tex]\[ x = 3.\overline{3} \][/tex] or approximately [tex]\( x = 3.333 \)[/tex].
Among the given options, the correct equation that can be used to find the input value at which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[ 1.8x - 10 = -4 ; x = \frac{10}{3} \][/tex]
However, note that [tex]\(\frac{10}{3}\)[/tex] is [tex]\( \approx 3.3333 \)[/tex], which matches our result. Thus, the correct solution is:
[tex]\[ 1.8x - 10 = -4 ; x = \frac{10}{3} \][/tex]
