Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

Describe each step used in solving the equation:

1. [tex]\( 9x - 4 = 7x + 8 \)[/tex]

2. [tex]\( -4x \)[/tex]

A. [tex]\( 2x - 4 = 8 \)[/tex]

B. [tex]\( 2x = 12 \)[/tex]

C. [tex]\( x = 6 \)[/tex]


Solve the equation and describe each step:

3. [tex]\( 2x = x + 9 \)[/tex]

4. [tex]\( 4 \)[/tex]

5. [tex]\( 7x = 5x + 24 \)[/tex]

6. [tex]\( 7 \)[/tex]

Sagot :

GinnyAnsweridn
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.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.