Answer :

GinnyAnswer
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]

Other Questions