14.1: Which One Doesn’t Belong: Equations
Which equation doesn’t belong?
$\frac12 x = \text50$
$\text60t = 30$
$x + 90 = \text100$
$\text0.01 = \text0.001x$
Let’s use all four operations with signed numbers to solve problems.
Which equation doesn’t belong?
$\frac12 x = \text50$
$\text60t = 30$
$x + 90 = \text100$
$\text0.01 = \text0.001x$
A tank of water is being drained. Due to a problem, the sensor does not start working until some time into the draining process. The sensor starts its recording at time zero when there are 770 liters in the tank.
Given that the drain empties the tank at a constant rate of 14 liters per minute, complete the table:
time after sensor starts (minutes) 
change in water (liters) 
expression 
water in 


row 1  0  0  $770 + (0) (\text14)$  770 
row 2  1  14  $770 + (1) (\text14) $  756 
row 3  5  70  
row 4  10 
Later, someone wants to use the data to find out how long the tank had been draining before the sensor started. Complete this table:
time after sensor starts (minutes) 
change in water (liters) 
expression  water in the tank (liters) 


row 1  1  14  $770 + (1) (\text14) $  756 
row 2  0  0  $770 + (0) (\text14) $  770 
row 3  1  14  $770 + (\text1) (\text14) $  784 
row 4  2  28  
row 5  3  
row 6  4  
row 7  5 
A utility company charges \$0.12 per kilowatthour for energy a customer uses. They give a credit of \$0.025 for every kilowatthour of electricity a customer with a solar panel generates that they don't use themselves.
A customer has a charge of \$82.04 and a credit of \$4.10 on this month's bill.
Find the value of the expression without a calculator.
\((2)(\text30)+(\text3)(\text20)+(\text6)(\text10) (2)(3)(10)\)
We can apply the rules for arithmetic with rational numbers to solve problems
In general:
$$a  b = a + (\text b)$$
If $a  b = x$, then $x + b = a$. We can add $\text b$ to both sides of this second equation to get that $x = a + (\text b)$
Remember: the distance between two numbers is independent of the order, but the difference depends on the order.
And when multiplying or dividing:
The sign of a positive number multiplied or divided by a negative number is always negative.
The sign of a negative number multiplied or divided by a positive number is always negative.
The sign of a negative number multiplied or divided by a negative number is always positive.