MHB Solve the following equations for a

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The discussion focuses on solving two algebraic equations for the variable a. For the first equation, 15/a = -10, the solution is found to be a = -3/2 after rearranging and simplifying. The second equation, (a + 5)/4 + (a - 6)/3 = 1/6, requires multiplying by the least common multiple to simplify, ultimately leading to the solution a = 11/7 after distributing and combining like terms. The participants confirm the steps and clarify the process, ensuring understanding of the algebra involved. Overall, the thread provides clear solutions and guidance for solving these equations.
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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.
 
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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
 

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