Step by step
The question
Question: Nadia has $8.
She saves $6 each week.
She wants at least $50.
How many weeks must she save?
1 Find what we know
What do we know?
At least $50.
$6 for each week.
At the start: $8.
What do we want?
How many weeks.
2 Name the unknown
We don't know how many weeks.
So we call it x.
At least $50 means $50 or more.
We write ≥ $50.
3 Write the inequality
In words: what the weeks add, plus the start, is at least $50.
So the inequality is 6x + 8 ≥ 50.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 6 and + 8.
The + 8 is on the outside, so it comes off first.
Then the times 6.
4 Remove the + 8
To remove + 8, we take away 8.
We do it on both sides, so the sign stays true.
+ 8 and − 8 make zero.
Cross them out.
50 − 8 = 42.
Now we have 6x ≥ 42.
5 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so the sign stays true.
6 divided by 6 is 1.
So just x is left.
42 divided by 6 is 7.
So x is greater than or equal to 7.
6 Show it on a number line
7 Answer the question
Weeks come in whole numbers.
7 is a whole number, so it stays.
Careful!
At least $50: exactly $50 is still OK.
So 7 weeks is fine.
So at least 7 weeks.
8 Check
Let's check in the story.
7 weeks: $50.
That is at least $50.
But 6 weeks would be $44: not enough.
So 7 is the fewest.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the inequality.
Then: solve it.
Then: answer the question.
Last: check.