Sure! Let's solve each of the provided equations step-by-step.
### 1. Solve the equation: [tex]\(9x - 4 = 7x + 8\)[/tex]
Step 1: Subtract [tex]\(7x\)[/tex] from both sides to get the [tex]\(x\)[/tex] terms on one side.
[tex]\[ 9x - 7x - 4 = 8 \][/tex]
Step 2: Simplify the left side.
[tex]\[ 2x - 4 = 8 \][/tex]
Step 3: Add 4 to both sides to isolate the [tex]\(2x\)[/tex] term.
[tex]\[ 2x - 4 + 4 = 8 + 4 \][/tex]
[tex]\[ 2x = 12 \][/tex]
Step 4: Divide both sides by 2 to solve for [tex]\(x\)[/tex].
[tex]\[ x = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
### 2. Solve the equation: [tex]\(-4x = 8\)[/tex]
Step 1: Divide both sides by -4 to isolate [tex]\(x\)[/tex].
[tex]\[ x = \frac{8}{-4} \][/tex]
[tex]\[ x = -2 \][/tex]
### Solve the equation and describe each step:
### 4. Solve the equation: [tex]\(2x = x + 9\)[/tex]
Step 1: Subtract [tex]\(x\)[/tex] from both sides to isolate the [tex]\(x\)[/tex] terms.
[tex]\[ 2x - x = 9 \][/tex]
[tex]\[ x = 9 \][/tex]
### 5. Solve the equation: [tex]\(4 = 4\)[/tex]
This equation is always true, and it doesn't depend on the value of [tex]\(x\)[/tex]. This is called an identity, meaning this equation is true for all values of [tex]\(x\)[/tex].
### 7. Solve the equation: [tex]\(7x = 5x + 24\)[/tex]
Step 1: Subtract [tex]\(5x\)[/tex] from both sides to isolate the [tex]\(x\)[/tex] terms.
[tex]\[ 7x - 5x = 24 \][/tex]
[tex]\[ 2x = 24 \][/tex]
Step 2: Divide both sides by 2 to solve for [tex]\(x\)[/tex].
[tex]\[ x = \frac{24}{2} \][/tex]
[tex]\[ x = 12 \][/tex]
### 8. Solve the equation: [tex]\(8 = 8\)[/tex]
This equation is also an identity, similar to equation 5, and it is true for all values of [tex]\(x\)[/tex].
In conclusion:
- The solution for [tex]\(9x - 4 = 7x + 8\)[/tex] is [tex]\(x = 6\)[/tex].
- The solution for [tex]\(-4x = 8\)[/tex] is [tex]\(x = -2\)[/tex].
- The solution for [tex]\(2x = x + 9\)[/tex] is [tex]\(x = 9\)[/tex].
- The equation [tex]\(4 = 4\)[/tex] is always true.
- The solution for [tex]\(7x = 5x + 24\)[/tex] is [tex]\(x = 12\)[/tex].
- The equation [tex]\(8 = 8\)[/tex] is always true.
