Sure, let's solve both equations step-by-step.
### Solution for [tex]\( 12 - 6 x + 34 x = 2 x - 24 \)[/tex]
1. Combine like terms:
On the left-hand side, combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
12 - 6x + 34x = 12 + 28x
\][/tex]
Now, we have:
[tex]\[
12 + 28x = 2x - 24
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side:
Subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
12 + 28x - 2x = -24
\][/tex]
Simplifying this, we get:
[tex]\[
12 + 26x = -24
\][/tex]
3. Isolate [tex]\(x\)[/tex]:
Subtract 12 from both sides:
[tex]\[
26x = -24 - 12
\][/tex]
Simplifying further:
[tex]\[
26x = -36
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 26:
[tex]\[
x = \frac{-36}{26} = \frac{-18}{13}
\][/tex]
So, the solution for the first equation is:
[tex]\[
x = -\frac{18}{13}
\][/tex]
### Solution for [tex]\( 6 x + 3 x = 4 - 5(2 x - 3) \)[/tex]
1. Simplify both sides:
Combine the terms involving [tex]\(x\)[/tex] on the left-hand side:
[tex]\[
6x + 3x = 9x
\][/tex]
Now, we have:
[tex]\[
9x = 4 - 5(2x - 3)
\][/tex]
2. Distribute the -5:
Expand the right-hand side:
[tex]\[
9x = 4 - 10x + 15
\][/tex]
Simplify by combining constants:
[tex]\[
9x = 19 - 10x
\][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side:
Add [tex]\(10x\)[/tex] to both sides:
[tex]\[
19x = 19
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 19:
[tex]\[
x = \frac{19}{19} = 1
\][/tex]
So, the solution for the second equation is:
[tex]\[
x = 1
\][/tex]
### Summary
- The solution for the equation [tex]\( 12 - 6 x + 34 x = 2 x - 24 \)[/tex] is [tex]\( x = -\frac{18}{13} \)[/tex].
- The solution for the equation [tex]\( 6 x + 3 x = 4 - 5(2 x - 3) \)[/tex] is [tex]\( x = 1 \)[/tex].
