Question

Match each definition to the correct word. (All words will be used only once)

Question 1 options:

A value, or values, we can put in place of a variable (such as x) that makes the equation true.


A fixed value. Terms with no variables

Example: The 7 in: 4x + 7


A letter or symbol that represents a missing value.

Example: The x in 4x + 7


The number multiplied by the variable (the number in front of the variable)

Example: The 4 in 4x + 7


Terms with the same variable, raised to the same power

1.
Variable

2.
Constant

3.
Coefficient

4.
Like Terms

5.
Solution

Answer 1

Simplify -9(x+3)+15x

Answer 2

What are the correct two steps, in the correct order, that would allow you to solve for x in the following equation?


Question 3 options:

+3 to both sides, then
2 on both sides


2 on both sides, then +3 on both sides


-3 to both sides, then x2 on both sides


x2 on both sides, then -3 on both side

Answer 3

2x-3=1

Answer 4

John and Josh were both solving the same equation. When they compared answers, John got x=1, and Josh got x=-5. Who was correct?

The equation that they both tried to solve was: 4x - 3 = 5x + 2

Question 4 options:

John


Josh


They are both wrong.

Answer 5

Which of the following is equivalent to 3x-4y=6

Answer 6

Here are the definitions matched with the correct words:

1. A value, or values, we can put in place of a variable (such as x) that makes the equation true.
**5. Solution**

2. A fixed value. Terms with no variables
**2. Constant**

3. A letter or symbol that represents a missing value.
**1. Variable**

4. The number multiplied by the variable (the number in front of the variable)
**3. Coefficient**

5. Terms with the same variable, raised to the same power
**4. Like Terms**

Answer 7

To simplify the expression \(-9(x + 3) + 15x\), follow these steps:

1. Distribute \(-9\) to both terms inside the parentheses:
\[
-9(x) - 9(3) + 15x = -9x - 27 + 15x
\]

2. Combine like terms \(-9x\) and \(15x\):
\[
(-9x + 15x) - 27 = 6x - 27
\]

So, the simplified expression is:
\[
6x - 27
\]

Answer 8

To solve for \(x\) in an equation that involves \(x^2\) and any constant, the correct steps typically involve isolating \(x^2\) first (if it’s added to a constant), and then taking the square root (which is often represented by the expression \(x^2\)) afterwards. However, the specific equation isn't provided, but based on common practices, the likely arrangement of solving based on your provided options would be:

1. **-3 to both sides, then x^2 on both sides**

This implies that you would first remove a constant on one side to isolate the \(x^2\) term before applying the square root to find \(x\).

Please specify the equation if you want tailored steps for your specific context!

Answer 9

To solve the equation \(2x - 3 = 1\), you can follow these two steps:

1. **Add 3 to both sides**: This will help you isolate the term with \(x\).
\[
2x - 3 + 3 = 1 + 3
\]
Which simplifies to:
\[
2x = 4
\]

2. **Divide both sides by 2**: This will solve for \(x\).
\[
\frac{2x}{2} = \frac{4}{2}
\]
Which simplifies to:
\[
x = 2
\]

So, the solution to the equation \(2x - 3 = 1\) is \(x = 2\).

### Step-by-step summary:
- **Add 3 to both sides:** \(2x = 4\)
- **Divide both sides by 2:** \(x = 2\)

This corresponds with the first set of mini-steps you provided: "+3 to both sides, then 2 on both sides" when you apply them correctly to isolate \(x\).

Answer 10

Let's solve the equation \(4x - 3 = 5x + 2\) to determine who, if anyone, was correct.

1. Start with the original equation:
\[
4x - 3 = 5x + 2
\]

2. Subtract \(4x\) from both sides to get all terms involving \(x\) on one side:
\[
-3 = 5x - 4x + 2
\]
Simplifying gives:
\[
-3 = x + 2
\]

3. Next, subtract \(2\) from both sides to isolate \(x\):
\[
-3 - 2 = x
\]
This simplifies to:
\[
-5 = x
\]
or:
\[
x = -5
\]

Based on this solution, Josh's answer is correct. Thus, the answer to the question is:

**Josh**

Answer 11

To express the equation \(3x - 4y = 6\) in different forms, we can manipulate it into various equivalent expressions. Here are a few common alternatives:

1. **Slope-Intercept Form (\(y = mx + b\))**: This is the form where \(m\) is the slope and \(b\) is the y-intercept.

Start by isolating \(y\):

\[
3x - 4y = 6
\]
Subtract \(3x\) from both sides:

\[
-4y = -3x + 6
\]
Now, divide every term by \(-4\):

\[
y = \frac{3}{4}x - \frac{3}{2}
\]

2. **Standard Form (\(Ax + By = C\))**: You already have it in this form, where \(A = 3\), \(B = -4\), and \(C = 6\).

3. **Intercepts Form**: You can express the original equation in terms of the x-intercept and y-intercept. To find the intercepts:
- **X-intercept** (set \(y = 0\)):
\[
3x - 4(0) = 6 \quad \Rightarrow \quad 3x = 6 \quad \Rightarrow \quad x = 2
\]
- **Y-intercept** (set \(x = 0\)):
\[
3(0) - 4y = 6 \quad \Rightarrow \quad -4y = 6 \quad \Rightarrow \quad y = -\frac{3}{2}
\]
Therefore, the intercept form is:
\[
x = 2 \text{ (x-intercept)} \quad \text{and} \quad y = -\frac{3}{2} \text{ (y-intercept)}
\]

If you have specific options provided for the equivalent forms, please share them, and I can help determine which one is equivalent to \(3x - 4y = 6\).