Solve linear algebra equation 2x – 1 = 9 – 3x

In summary, the first problem is solved by getting all the x's on one side and all the numbers on the other side, and then solving for x. The second problem involves expanding parentheses and combining like terms before solving for b. Both problems result in x = 2 and b = 9.
  • #1
gazparkin
17
0
Hi,

Could someone help me with this question:

2x – 1 = 9 – 3x

Thank you in advance!
 
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  • #2
gazparkin said:
Hi,

Could someone help me with this question:

2x – 1 = 9 – 3x

Thank you in advance!

Sorry, there's another one that I'm stuck on too. Really interested to understand the working out on this.

4(3b-1)+6=5(2b+4)
 
  • #3
gazparkin said:
Hi,

Could someone help me with this question:

2x – 1 = 9 – 3x

Thank you in advance!
Step 1: Get all the x's on one side: Subtract 2x on both sides:
2x - 1 - 2x = 9 - 3x - 2x

-1 = 9 - 5x

Now do the same with the numbers. Can you finish?

-Dan

- - - Updated - - -

gazparkin said:
Sorry, there's another one that I'm stuck on too. Really interested to understand the working out on this.

4(3b-1)+6=5(2b+4)
Expand the parentheses:
4(3b - 1) + 6 = 5(2b + 4)

\(\displaystyle 4 \cdot 3b + 4 \cdot (-1) + 6 = 5 \cdot 2b + 5 \cdot 4\)

Now combine terms:
12b - 4 + 6 = 10b + 20

12b + 2 = 10b + 20

Now it's like your first problem. Can you finish?

-Dan
 
  • #4
topsquark said:
Step 1: Get all the x's on one side: Subtract 2x on both sides:
2x - 1 - 2x = 9 - 3x - 2x

-1 = 9 - 5x

Now do the same with the numbers. Can you finish?

-Dan

- - - Updated - - -Expand the parentheses:
4(3b - 1) + 6 = 5(2b + 4)

\(\displaystyle 4 \cdot 3b + 4 \cdot (-1) + 6 = 5 \cdot 2b + 5 \cdot 4\)

Now combine terms:
12b - 4 + 6 = 10b + 20

12b + 2 = 10b + 20

Now it's like your first problem. Can you finish?

-Dan
Thanks Dan - makes this really clear. The first one I get x=4 and the 2nd one I get b=9.
 
  • #5
gazparkin said:
Thanks Dan - makes this really clear. The first one I get x=4 and the 2nd one I get b=9.
The second one is okay. Let's take another look at the first one. I left off with
-1 = 9 - 5x

Now get the numbers:
-1 - 9 = 9 - 5x - 9

-10 = -5x

\(\displaystyle \dfrac{-10}{-5} = \dfrac{-5x}{-5} \)

2 = x

-Dan
 

Related to Solve linear algebra equation 2x – 1 = 9 – 3x

1. What is a linear algebra equation?

A linear algebra equation is a mathematical statement that involves variables, constants, and operations such as addition, subtraction, multiplication, and division. It can be written in the form of ax + b = c, where a, b, and c are constants and x is the variable.

2. How do I solve a linear algebra equation?

To solve a linear algebra equation, you need to isolate the variable on one side of the equation by performing the same operation on both sides. In the given equation 2x - 1 = 9 - 3x, you can add 3x to both sides to get 5x - 1 = 9. Then, add 1 to both sides to get 5x = 10. Finally, divide both sides by 5 to get the solution x = 2.

3. What is the importance of solving linear algebra equations?

Linear algebra equations are used to solve real-world problems in various fields such as physics, engineering, economics, and computer science. They help in understanding and analyzing relationships between variables and making predictions based on given data.

4. Can I use a calculator to solve a linear algebra equation?

Yes, you can use a calculator to solve a linear algebra equation. However, it is important to understand the steps involved in solving the equation manually to ensure accuracy and to be able to apply the concept to different problems.

5. Are there any tips for solving linear algebra equations?

One helpful tip is to always perform the same operation on both sides of the equation to maintain balance. It is also important to pay attention to the signs of the terms and to combine like terms to simplify the equation. Additionally, checking your solution by substituting it back into the original equation can help verify its accuracy.

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