Solve the following equations for a

  • Context: MHB 
  • Thread starter Thread starter lmae
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around solving two algebraic equations for the variable 'a'. Participants seek assistance with the equations, exploring both the methods of solving them and the clarity of the solutions provided.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents two equations to solve for 'a': Q1: 15/a = -10 and Q2: (a + 5)/4 + (a - 6)/3 = 1/6.
  • Another participant provides a solution for Q1, stating that after rearranging, a = -3/2.
  • The same participant suggests multiplying through by the least common multiple for Q2 and provides the equation 3(a + 5) + 4(a - 6) = 2 as a next step.
  • A later reply expresses gratitude for the help with Q1 but indicates confusion regarding whether the provided steps for Q2 lead to a final answer.
  • Further steps are shown for Q2, leading to the conclusion that a = 11/7 after combining like terms and isolating 'a'.

Areas of Agreement / Disagreement

Participants generally agree on the steps taken for Q1, but there is uncertainty regarding the completeness of the solution for Q2, as one participant questions whether further work is needed.

Contextual Notes

The discussion includes various steps and methods for solving the equations, but there is no consensus on whether the solution for Q2 is final or requires additional steps.

lmae
Messages
8
Reaction score
0
Hi folks,

Need some help on the following equations. I have never been great with maths, algebra especially, and am struggling to understand.Solve the following equation for a:
Q1: 15/a=-10

Q2: Solve for a in the equation: a+5/4+a-6/3=1/6

Any help is greatly appreciated.
 
Mathematics news on Phys.org
Hi lmae and welcome to MHB! :D

Q1:

15/a = -10

Multiply through by a:

15 = -10a

Rearrange and simplify:

a = -15/10 = -3/2

Make sense?

Q2: Solve for a in the equation: (a + 5)/4 + (a - 6)/3 = 1/6

Multiply through by the least common multiple of 4 and 3, which is 12:

3(a + 5) + 4(a - 6) = 2

O.k? Can you continue?
 
Hi,

Thanks very much for the help. The first now makes total sense to me and was able to complete a whole bunch correctly, so a big thanks!

The second one I am still struggling with. Is that the final answer there? Or should I be doing more working out to get to another answer?
 
3(a + 5) + 4(a - 6) = 2

Distribute:

3 * a + 3 * 5 + 4 * a - 4 * 6 = 2

3a + 15 + 4a - 24 = 2

Combine like terms:

3a + 4a + 15 - 24 = 2

7a - 9 = 2

7a = 2 + 9

7a = 11

a = 11/7
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K