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

Question

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

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 2

Simplify -9(x+3)+15x

Answer 3

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 4

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 5

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 6

2x-3=1

Answer 7

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 8

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 9

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 10

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

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 \(3x - 4y = 6\).