Mathematics began long before the symbols we use today came into existence. The early civilizations needed to count goods, measure land, predict seasons, and organize construction projects. Over time, mere numbers were not sufficient; it was also necessary to find unknown quantities. This is how the initial ideas that would eventually lead to algebra gradually emerged.
One of the great interests of mathematics is its ability to transform an unknown situation into a problem that can be solved methodically. This way of reasoning has led to remarkable achievements in architecture, astronomy, navigation, engineering, and today, in computing and modern technologies.
“Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is one country.” — David Hilbert
Equations with multiple parentheses can seem complicated even before you start. However, when approached calmly, step by step, they become much more manageable. The key is not to rush to find the value of x immediately: first, simplify the equation, then progressively isolate the unknown.
What This Challenge Allows You to Work On:
- Solving an equation;
- Finding an unknown;
- Distributive property;
- Removing parentheses;
- Managing negative signs;
- Grouping like terms;
- Mental calculation;
- Verifying a solution;
- Logic and concentration.
DAILY CHALLENGE!
What is the value of x in the following equation?
Pay close attention to the parentheses and especially the sign before the second one.
You have 30 seconds!
The Countdown Begins
40…
30…
25…
20…
15…
10…
5…
4…
3…
2…
1…
Time’s up!
What Your Performance Can Reveal
Result found quickly and correctly, you have excellent logic and good analytical skills.
Result found after some thought, you know how to structure your reasoning and verify your steps.
And if the result was incorrect or not found, no worries; this type of exercise is perfect for improving method and precision.
Detailed Solution We Found (Not Necessarily the Only One, Sometimes Even the Right One)
We start with the equation:
3(x + 5) − 2(x − 3) = 20
Let’s begin by expanding the parentheses.
For the first:
3(x + 5) = 3x + 15
For the second, be careful with the negative sign:
−2(x − 3) = −2x + 6
The equation then becomes:
3x + 15 − 2x + 6 = 20
Let’s group like terms:
3x − 2x + 15 + 6 = 20
Which gives:
x + 21 = 20
To isolate x, we subtract 21 from both sides:
x = 20 − 21
Therefore:
Answer: x = −1
Let’s verify our result in the original equation:
3(−1 + 5) − 2(−1 − 3) = 20
3 × 4 − 2 × (−4) = 20
12 + 8 = 20
20 = 20
The value x = −1 is indeed correct.
Conclusion
This challenge reminds us that an equation that seems long is not necessarily difficult. Here, the key point was to properly distribute the numbers in front of the parentheses, especially the −2, which changes the −3 into +6.
Once the parentheses are correctly removed, the equation becomes very simple. This is a good illustration of an essential principle in mathematics: proceeding in the right order and verifying each transformation often allows for the simplification of a problem that initially seemed complicated.
And before you get lost in the depths of the web, explore more games and tests by clicking here.
