To solve the equation [tex]\( 130 + 56x = 214 \)[/tex] and find out how many hours the plumber worked, we need to isolate the variable term [tex]\( x \)[/tex].
Step 1: To isolate the variable term [tex]\( 56x \)[/tex], we should first eliminate the fixed cost of [tex]\( \$130 \)[/tex]. This can be done by subtracting [tex]\( 130 \)[/tex] from both sides of the equation.
So, we perform the subtraction:
[tex]\[
130 + 56x - 130 = 214 - 130
\][/tex]
Simplifying this, we get:
[tex]\[
56x = 84
\][/tex]
Step 2: Next, we need to solve for [tex]\( x \)[/tex]. To do this, we will divide both sides of the equation by [tex]\( 56 \)[/tex] because the variable term [tex]\( 56x \)[/tex] means 56 times [tex]\( x \)[/tex].
So, we perform the division:
[tex]\[
\frac{56x}{56} = \frac{84}{56}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 1.5
\][/tex]
Therefore, the plumber worked for [tex]\( 1.5 \)[/tex] hours.
