Question

match the property of equality with the example that models the property.

addition property of equality.
multiplication property of equality.
subtraction property of equality.
division property of equality.

3x-4+4=12+4
(1/2)+5x-(1/2)=8-(1/2)
(4x)(1/4)=(3)(1/4)
55/11=11x/11

Answer 1

PERFECT now The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.

How many credit hours will a student have to take for the two tuition costs to be equal? Round the answer to the nearest tenth of an hour.

250 + 200h = 300 + 180h
250 + 200h = 300 + 180h
− 180h − 180h
250 + 20h = 300

Answer 2

AWESOME 2.5

solve the equation -7x+12-2x= 23+13x

Simplify by combining like terms that are one the same side of the equation. Which terms can be combined?

Answer 3

Okay if anyone is seeing this these are the answers "-7x and -2x" then we have "Subtract 12" then "subtracting 13x from" and at last "divide -22" you should get x=-1/2

solve the equation 2/3-4x+7/2=-9x+5/6 whats the first step??

Answer 4

okay i combined terms now what? add subtract multiply or divide?

Answer 5

okay when i combined terms it gave me 25/6-4x=-9x+5/6 and i think you said to add 9 so it gave me 79/6-4x=-9x+59/6 so whats the next step?? did i do something wrong? or is it good still

Answer 6

Sure! Here’s the matching of each property of equality with its corresponding example:

1. **Addition Property of Equality**
- **Example:** \(3x - 4 + 4 = 12 + 4\)
(This shows that adding the same amount to both sides keeps the equation balanced.)

2. **Subtraction Property of Equality**
- **Example:** \((1/2) + 5x - (1/2) = 8 - (1/2)\)
(This demonstrates that subtracting the same amount from both sides maintains equality.)

3. **Multiplication Property of Equality**
- **Example:** \((4x)(1/4) = (3)(1/4)\)
(This example illustrates that multiplying both sides by the same non-zero number keeps the equation balanced.)

4. **Division Property of Equality**
- **Example:** \(55/11 = 11x/11\)
(This shows that dividing both sides by the same non-zero number preserves equality.)

Let me know if you have any other questions!

Answer 7

To find the number of credit hours \( h \) for which the tuition costs for the community college and the state university are equal, we set the two functions equal:

\[
C(h) = S(h)
\]
\[
250 + 200h = 300 + 180h
\]

Now, let's solve for \( h \).

1. Subtract \( 180h \) from both sides:
\[
250 + 200h - 180h = 300
\]
\[
250 + 20h = 300
\]

2. Next, subtract \( 250 \) from both sides:
\[
20h = 300 - 250
\]
\[
20h = 50
\]

3. Now, divide both sides by \( 20 \):
\[
h = \frac{50}{20} = 2.5
\]

Thus, the number of credit hours a student needs to take for the two tuition costs to be equal is **2.5 hours** (rounded to the nearest tenth).

Answer 8

Let's solve the equation step by step:

The equation is:
\[
-7x + 12 - 2x = 23 + 13x
\]

### Step 1: Combine Like Terms on Each Side

**Left Side:**
- Combine the \( -7x \) and \( -2x \):
\[
-7x - 2x + 12 = -9x + 12
\]

**Right Side:**
- There are no like terms to combine on the right side:
\[
23 + 13x
\]

So we can rewrite the equation as:
\[
-9x + 12 = 23 + 13x
\]

### Step 2: Rearranging the Equation

Now, we can start moving the terms involving \( x \) to one side and the constant terms to the other side:

### Step 3: Move \( 13x \) to the Left Side

Subtract \( 13x \) from both sides:
\[
-9x - 13x + 12 = 23
\]
This simplifies to:
\[
-22x + 12 = 23
\]

### Step 4: Move the Constant Term (12) to the Right Side

Subtract \( 12 \) from both sides:
\[
-22x = 23 - 12
\]
This simplifies to:
\[
-22x = 11
\]

### Step 5: Divide by -22

Now, divide both sides by \( -22 \):
\[
x = \frac{11}{-22}
\]
This simplifies to:
\[
x = -\frac{1}{2}
\]

### Conclusion

The solution to the equation \(-7x + 12 - 2x = 23 + 13x\) is:
\[
x = -\frac{1}{2}
\]

### Summary of Combining Like Terms

- On the left side, you combined \( -7x \) and \( -2x \) to get \( -9x \).
- There were no like terms to combine on the right side.

Let me know if you have any more questions!

Answer 9

Let's start solving the equation step by step:

The equation is:
\[
\frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6}
\]

### First Step: Combine Like Terms on Each Side

To proceed, the first step is to combine the constant terms on the left side of the equation. The constants we have on the left side are \(\frac{2}{3}\) and \(\frac{7}{2}\).

#### Finding a Common Denominator

The denominators here are 3 and 2. The least common denominator (LCD) of 3 and 2 is 6. We need to convert the fractions:

1. Convert \(\frac{2}{3}\) to a denominator of 6:
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]

2. Convert \(\frac{7}{2}\) to a denominator of 6:
\[
\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}
\]

Now we can combine the constants on the left side:
\[
\frac{4}{6} + \frac{21}{6} = \frac{4 + 21}{6} = \frac{25}{6}
\]

### Rewrite the Equation

Now we can rewrite the equation as:
\[
\frac{25}{6} - 4x = -9x + \frac{5}{6}
\]

### Next Steps

From here, you can either move the term with \(x\) to one side and the constant term to the other, or isolate \(x\).

The next step could be either:
- **Add \(9x\) to both sides:**
\[
\frac{25}{6} - 4x + 9x = \frac{5}{6}
\]
Simplifying gives you:
\[
\frac{25}{6} + 5x = \frac{5}{6}
\]

Or, you could choose to subtract \(\frac{25}{6}\) from both sides to isolate the terms with \(x\).

Would you like to continue solving from here, or would you prefer a different approach? Let me know!

Answer 10

Great! You've combined the terms on the left side. Now, let's continue solving the equation.

You should now have:
\[
\frac{25}{6} - 4x = -9x + \frac{5}{6}
\]

### Step 1: Isolate the variable terms on one side

To isolate the variable terms on one side, you can add \(9x\) to both sides:

\[
\frac{25}{6} - 4x + 9x = \frac{5}{6}
\]

This simplifies to:

\[
\frac{25}{6} + 5x = \frac{5}{6}
\]

### Step 2: Isolate \(x\)

Next, subtract \(\frac{25}{6}\) from both sides to get the \(x\) term alone:

\[
5x = \frac{5}{6} - \frac{25}{6}
\]

Combine the fractions on the right side:

\[
5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3}
\]

### Step 3: Divide by the coefficient of \(x\)

Now, divide both sides by \(5\) to solve for \(x\):

\[
x = \frac{-10/3}{5} = \frac{-10}{3 \times 5} = \frac{-10}{15} = \frac{-2}{3}
\]

### Conclusion

Thus, the solution to the equation \( \frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6} \) is:

\[
x = -\frac{2}{3}
\]

Let me know if you have any questions or if there's anything else you need help with!

Answer 11

Let's clarify what happened after combining the terms. Based on your last message, it seems there might have been a miscalculation while adding or subtracting the constants. Let's break it down step-by-step, starting from the correct combined equation.

### Starting Point

You correctly combined the terms, resulting in:
\[
\frac{25}{6} - 4x = -9x + \frac{5}{6}
\]

### Step 1: Isolate the Variable Terms

Now, to isolate the \(x\) terms, we want to combine the terms involving \(x\). We can add \(9x\) to both sides:
\[
\frac{25}{6} - 4x + 9x = \frac{5}{6}
\]
This results in:
\[
\frac{25}{6} + 5x = \frac{5}{6}
\]

At this point, you did not change the constants, so let's ensure understanding.

### Step 2: Keep Isolating \(x\)

Now subtract \(\frac{25}{6}\) from both sides:
\[
5x = \frac{5}{6} - \frac{25}{6}
\]

Combine the fractions on the right side:
\[
5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3}
\]

### Step 3: Divide to Solve for \(x\)

Now, divide both sides by \(5\) to solve for \(x\):
\[
x = \frac{-10/3}{5} = \frac{-10}{15} = \frac{-2}{3}
\]

### Conclusion

So, the final answer remains:
\[
x = -\frac{2}{3}
\]

If you feel uncertain about any step or if there’s a specific part of the calculation process that seems off, please let me know, and I’ll be happy to clarify further!