Step by step
The question
Question: Ana has $50.
She saves $10 each week.
She wants at least $40.
How many weeks must she save?
1 Find what we know
What do we know?
At least $40.
$10 for each week.
At the start: $50.
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 $40 means $40 or more.
We write ≥ $40.
3 Write the inequality
In words: what the weeks add, plus the start, is at least $40.
So the inequality is 10x + 50 ≥ 40.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 10 and + 50.
The + 50 is on the outside, so it comes off first.
Then the times 10.
4 Remove the + 50
To remove + 50, we take away 50.
We do it on both sides, so the sign stays true.
+ 50 and − 50 make zero.
Cross them out.
40 − 50 = −10.
Now we have 10x ≥ −10.
5 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so the sign stays true.
10 divided by 10 is 1.
So just x is left.
−10 divided by 10 is −1.
So x is greater than or equal to −1.
6 Show it on a number line
7 Answer the question
x ≥ −1: even 0 weeks works.
The goal is reached already.
So there is no answer to find.
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the inequality.
Then: solve it.
Last: answer the question.