Sure, let's solve each of the equations step-by-step:
### Part a) Solve [tex]\(2(x+3) = x-4\)[/tex]
1. Expand the left side:
[tex]\[
2(x+3) = 2x + 6
\][/tex]
So the equation becomes:
[tex]\[
2x + 6 = x - 4
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side by subtracting [tex]\(x\)[/tex] from both sides:
[tex]\[
2x + 6 - x = x - 4 - x
\][/tex]
Simplifying this gives:
[tex]\[
x + 6 = -4
\][/tex]
3. Isolate [tex]\(x\)[/tex] by subtracting 6 from both sides:
[tex]\[
x + 6 - 6 = -4 - 6
\][/tex]
Simplifying this gives:
[tex]\[
x = -10
\][/tex]
So the solution to part a) is:
[tex]\[
x = -10
\][/tex]
### Part b) Solve [tex]\(4(5x - 2) = 2(9x + 3)\)[/tex]
1. Expand both sides:
[tex]\[
4(5x - 2) = 20x - 8
\][/tex]
[tex]\[
2(9x + 3) = 18x + 6
\][/tex]
So the equation becomes:
[tex]\[
20x - 8 = 18x + 6
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side by subtracting [tex]\(18x\)[/tex] from both sides:
[tex]\[
20x - 18x - 8 = 18x - 18x + 6
\][/tex]
Simplifying this gives:
[tex]\[
2x - 8 = 6
\][/tex]
3. Isolate [tex]\(x\)[/tex] by adding 8 to both sides:
[tex]\[
2x - 8 + 8 = 6 + 8
\][/tex]
Simplifying this gives:
[tex]\[
2x = 14
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{14}{2}
\][/tex]
Simplifying this gives:
[tex]\[
x = 7
\][/tex]
So the solution to part b) is:
[tex]\[
x = 7
\][/tex]
In summary:
- For part a), [tex]\(x = -10\)[/tex]
- For part b), [tex]\(x = 7\)[/tex]
