In chemistry, we use equations that express the relationship between certain variables. Let’s
look at how we would solve for x in the following equation:
2x + 8 = 14
Our overall goal is to rearrange the items in the equation to obtain x on one side.
- Place all/ike temJS on one side. The numbers 8 and 14 are like terms. To remove
the 8 from the left side of the equation, we subtract 8. To keep a balance, we need to
subtract 8 from the 14 on the other side.
2x + .8′ – .8′ = 14 – 8
2x = 6
- Isolate the variable you need to solve for. In this problem, we obtain x by dividing
both sides of the equation by 2. The value of x is the result when 6 is divided by 2.
Zr 6 z = 2
X = 3
- Check your answer. Check your answer by substituting your value for x back into
the original equation.
2(3) + 8 = 14
6 + 8 = 14
14 = 14 Your answer x = 3 is correct.
Summary: To solve an equation for a particular variable, be sure you perform the same
mathematical operations on both s ides of the equation.
If you eliminate a symbol or number by subtracting, you need to subtract that same
symbol or number from both sides.
If you eliminate a symbol or number by adding, you need to add that same symbol or
number to both sides.
If you cancel a symbol or number by dividing, you need to divide both sides by that
same symbol or number.
If you cancel a symbol or number by multiplying, you need to multiply both s ides by
that same symbol or number.
When we work with temperature, we may need to convert between degrees Celsius and
degrees Fahrenheit using the following equation:
- TF = 1.8(Tc) + 32
To obtain the equation for converting degrees Fahrenheit to degrees Celsius, we subtract
32 from both sides.
TF = 1.8(Tc) + 32
TF – 32 = 1.8(Tc) + n – n
TF – 32 = 1.8(Tc)
To obtain Tc by itself, we divide both sides by 1.8.
Tr – 32 M!'(Tc)
— = –= Tc