To review, an equation is a mathematical statement that two expressions are equal or have the same value. When solving an equation, you want to determine or solve for the value of the variable or unknown quantity. The first step in solving an equation is to combine like terms on either side of the equation. You can then use inverse operations to undo operations in the equation to isolate the variable.
There are several crucial steps in writing an equation to represent a situation:
IN CONTEXT
For her cellular phone service, Seylon pays $32 a month plus $0.75 for each minute over the allowed minutes in her plan. Seylon received a bill for $47 last month. How many minutes did she use her phone beyond the allowed minutes?
You want to know how many minutes she used over the allowed minutes, so this unknown quantity will be your variable. Therefore you can define x as the number of minutes used over her allowance.
Using the given information and a variable, you know that Seylon pays $32 per month plus an additional $0.75—or 0.75 dollars—for every minute used over the allowance. Therefore, you will need to multiply 0.75 times your variable, x. You also know that 32 plus 0.75x will equal the total amount paid, $47. It follows, then, that your equation is:
To solve this equation, you want to isolate your x variable. Start by subtracting 32 from each side of the equation, which simplifies the expression to:
Next, divide by 0.75 on both sides of the equation, which provides the solution of x equals 20.
This means that Seylon used 20 minutes over her allowance, which seems like a reasonable solution, as it’s not a negative number or an excessively big number. You can verify that your solution is correct by substituting it back into the original equation. This translates to:
Using the order of operations, you can simplify the left side of the equation, starting with multiplication and moving on to addition. 0.75 times 20 equals 15, plus 32, equals 47. Therefore, your equation is 47 equals 47. This is a true statement, which means your solution of x equals 20 is correct.
Source: This work is adapted from Sophia author Colleen Atakpu.