Question

select the TWO expressions that are equivalent to the given expression.
(2x+2) -(3x+11)
a. 2x-3x+2-11
b. 5x+13
c. -x-9
d. -x+9
e. 5x+9
f. -x+13
g. 2x-3x+2+11
Answer
simplify the expression
6(3x-5)+2(3x-5)-8(2x-5)
a.8x
b.24x-40
c.36x-60
d.48x-80
Answer
determine the unknown number
twice a number, increased by 3 is 7.
a. the number is 5
b. the number is 20
c. the number is 8
d. the number is 2
i think the answer is d am i correct?
Answer
solve for x and tell me the steps
3x-7-2x+5=6
a.x=7
b.x=-8
c.x=8
d.x=4
Answer
do i use one more operation to solve for x or do i use two more operations to solve for x
Answer
tickets to the baseball game are on sale for $1.50 off the regular price. dea buys 6 tickets if her total is $ 51 how much is the regular price of each ticket
a. $8.75
b. $8.25
c. $10.00
d. $7.00
think the answer is d
Answered by GPT-4o mini
To solve the expression \((2x + 2) - (3x + 11)\), we first need to distribute the negative sign to the second expression:

\[
(2x + 2) - (3x + 11) = 2x + 2 - 3x - 11
\]

Now we can combine like terms:

\[
2x - 3x + 2 - 11 = -x - 9
\]

So the equivalent expression is \(-x - 9\).

Now, let’s evaluate the provided options:

a. \(2x - 3x + 2 - 11 = -x - 9\) (equivalent)

b. \(5x + 13\) (not equivalent)

c. \(-x - 9\) (equivalent)

d. \(-x + 9\) (not equivalent)

e. \(5x + 9\) (not equivalent)

f. \(-x + 13\) (not equivalent)

g. \(2x - 3x + 2 + 11 = -x + 13\) (not equivalent)

The two equivalent expressions are:
- a. \(2x - 3x + 2 - 11\)
- c. \(-x - 9\)
Answered by GPT-4o mini
To simplify the expression \(6(3x - 5) + 2(3x - 5) - 8(2x - 5)\), we will distribute the constants and then combine like terms.

**Step 1: Distribute**

1. \(6(3x - 5) = 18x - 30\)
2. \(2(3x - 5) = 6x - 10\)
3. \(-8(2x - 5) = -16x + 40\)

Now substituting these back into the expression:

\[
(18x - 30) + (6x - 10) + (-16x + 40)
\]

**Step 2: Combine Like Terms**

Now, combine all the \(x\) terms and the constant terms:

1. Combine the \(x\) terms:
\[
18x + 6x - 16x = (18 + 6 - 16)x = 8x
\]

2. Combine the constant terms:
\[
-30 - 10 + 40 = -30 - 10 + 40 = 0
\]

**Final Result:**

The simplified expression is:

\[
8x
\]

Thus, the answer is **a. \(8x\)**.
Answered by GPT-4o mini
Let's denote the unknown number as \( x \). According to the problem, "twice a number, increased by 3 is 7," we can write this as an equation:

\[
2x + 3 = 7
\]

Now, we will solve this equation step by step:

1. Subtract 3 from both sides:
\[
2x + 3 - 3 = 7 - 3
\]
This simplifies to:
\[
2x = 4
\]

2. Divide both sides by 2:
\[
x = \frac{4}{2} = 2
\]

So, the unknown number is \( x = 2 \).

You are correct! The answer is **d. the number is 2**.
Answered by GPT-4o mini
To solve the equation \(3x - 7 - 2x + 5 = 6\), we will follow these steps:

**Step 1: Combine like terms on the left-hand side.**

Starting with the equation:

\[
3x - 7 - 2x + 5 = 6
\]

Combine the \(x\) terms and the constant terms:

1. The \(x\) terms: \(3x - 2x = x\)
2. The constant terms: \(-7 + 5 = -2\)

So the equation simplifies to:

\[
x - 2 = 6
\]

**Step 2: Isolate \(x\).**

To isolate \(x\), add 2 to both sides:

\[
x - 2 + 2 = 6 + 2
\]

This simplifies to:

\[
x = 8
\]

**Final Answer:**

The solution for \(x\) is \(8\), so the correct answer is:

**c. \(x = 8\)**.
Answered by GPT-4o mini
In the context of solving the equation \(3x - 7 - 2x + 5 = 6\), once we simplify to \(x - 2 = 6\), you only need **one additional operation** to solve for \(x\).

Here's the breakdown:

1. **Combine Like Terms**: From \(3x - 7 - 2x + 5 = 6\) to \(x - 2 = 6\) (this counts as one operation).

2. **Isolate \(x\)**: Then you perform one more operation to isolate \(x\) by adding 2 to both sides, resulting in \(x = 8\).

So, in total, you typically perform **two operations** to go from the original equation to the final answer \(x = 8\):
1. Combine like terms
2. Isolate \(x\) (add 2)

Therefore, you used **two operations** overall but only **one additional operation** after combining like terms.
Answered by GPT-4o mini
Let the regular price of each ticket be \( p \). The discounted price per ticket is therefore \( p - 1.50 \).

Dea buys 6 tickets at this discounted price, and the total cost for 6 tickets is $51. We can set up the following equation:

\[
6(p - 1.50) = 51
\]

**Step 1: Distribute the 6.**

\[
6p - 9 = 51
\]

**Step 2: Add 9 to both sides to isolate the term with \( p \).**

\[
6p - 9 + 9 = 51 + 9
\]

This simplifies to:

\[
6p = 60
\]

**Step 3: Divide both sides by 6 to solve for \( p \).**

\[
p = \frac{60}{6} = 10
\]

Thus, the regular price of each ticket is **$10.00**.

So the correct answer is **c. $10.00**, not d. $7.00.