The discussion focuses on solving linear algebra equations, specifically 2x – 1 = 9 – 3x and 4(3b-1)+6=5(2b+4). The first equation simplifies to x = 2 after isolating x on one side. The second equation, after expanding and combining terms, leads to the solution b = 9. Dan provides step-by-step guidance on how to approach these problems, emphasizing the importance of isolating variables and combining like terms.
PREREQUISITESStudents learning algebra, educators teaching mathematics, and anyone seeking to improve their problem-solving skills in linear equations.
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:gazparkin said:Hi,
Could someone help me with this question:
2x – 1 = 9 – 3x
Thank you in advance!
Expand the parentheses: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)
Thanks Dan - makes this really clear. The first one I get x=4 and the 2nd one I get b=9.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)
[math]4 \cdot 3b + 4 \cdot (-1) + 6 = 5 \cdot 2b + 5 \cdot 4[/math]
Now combine terms:
12b - 4 + 6 = 10b + 20
12b + 2 = 10b + 20
Now it's like your first problem. Can you finish?
-Dan
The second one is okay. Let's take another look at the first one. I left off withgazparkin said:Thanks Dan - makes this really clear. The first one I get x=4 and the 2nd one I get b=9.