Solve the following equations for a

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In summary, to solve the equation (a + 5)/4 + (a - 6)/3 = 1/6, we first multiply both sides by the least common multiple of 4 and 3, which is 12. Then, we distribute and combine like terms to isolate the variable a, and finally solve for a to get the answer of 11/7.
  • #1
lmae
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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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  • #2
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?
 
  • #3
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?
 
  • #4
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
 

FAQ: Solve the following equations for a

What does it mean to solve an equation for a?

When you solve an equation for a, you are finding the value of the variable a that makes the equation true. This is also known as finding the solution or root of the equation.

How do I solve an equation for a?

To solve an equation for a, you need to isolate the variable a on one side of the equation. This can be done by performing the same operation on both sides of the equation until a is the only term on one side.

Can you give an example of an equation being solved for a?

Sure, let's say we have the equation 2a + 4 = 12. To solve for a, we need to isolate it on one side. We can start by subtracting 4 from both sides, which gives us 2a = 8. Then, we divide both sides by 2 to get a = 4. So, the solution to this equation is a = 4.

Are there any special rules or steps for solving equations for a?

Yes, there are a few important rules to keep in mind when solving equations for a. These include always performing the same operation on both sides of the equation, being careful with negative numbers, and checking your answer by plugging it back into the original equation.

Why is it important to be able to solve equations for a?

Solving equations for a is an essential skill in mathematics and science. It allows us to find the value of unknown quantities and make predictions about real-world situations. It is also the basis for more advanced mathematical concepts and problem-solving strategies.

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