How to solve this?

In the expression A(x+5)+2(-Bx+2), the coefficient of x is 17 and the constant term is 359. What is the value of A-B?

Note by Eka Kurniawan
7 years, 2 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

A(x+5) = Ax + 5A

2(-Bx+2) = -2Bx + 4

I A - 2B = 17 (coefficient of x)

II 5A + 4 = 359 (the constant term is 359)

II 5A = 355

A = 71

So.. I 71 - 2B = 17

2B = 54

B = 27

A - B = 71 - 27 = 44

Felipe Magalhães - 7 years, 2 months ago

A(x+5)+2(−Bx+2) A(x+5) + 2(-Bx + 2)

Opening the brackets, we get,

Ax+5A−2Bx+4 Ax + 5A - 2Bx + 4

Grouping Like terms together,

(A−2B)x+(5A+4) (A - 2B)x + (5A + 4)

Now, by the question,

A−2B=17,5A+4=359 A - 2B = 17, 5A + 4 = 359

Solving the second equation,

5A=355→A=71 5A = 355 \rightarrow A = 71

Putting the value of A in the first equation

71−2B=17→54=2B→B=27 71 - 2B = 17 \rightarrow 54 = 2B \rightarrow B = 27

To find, A−B=71−27=44 A - B = 71 - 27 = \boxed{44}

Siddhartha Srivastava - 7 years, 2 months ago

ooo, okay! now I understand what the question means

Eka Kurniawan - 7 years, 2 months ago
×

Problem Loading...

Note Loading...

Set Loading...