Step by step
The question
Question: A taxi charges $3 plus $2 per mile.
A ride costs $19.
How many miles was the ride?
1 Find what we know
What do we know?
$3 is paid one time.
$2 for each mile.
Altogether: $19.
What do we want?
How many miles.
2 Name the unknown
We don't know how many miles.
So we call it x.
3 Write the equation
In words: what the miles cost, plus the start, makes the total.
So the equation is 2x + 3 = 19.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 2 and + 3.
The + 3 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 3
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
19 − 3 = 16.
Now we have 2x = 16.
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
16 divided by 2 is 8.
So x = 8!
6 Answer the question
So the answer is 8 miles.
7 Check
Let's check in the story.
8 miles at $2 each: 8 times 2 is $16.
Plus the $3 at the start: $19, like the story says.
Does it make sense?
A whole number of miles.
And the total, $19, is more than the $3 start.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.