Question

What is the first step to solve the inequality x-5< x/6
• A. Divide both sides of the inequality by 6 to simplify: x/6 - 5/6 <6
• B. Divide both sides of the inequality by x to simplify: 1-5/x <6
C. Multiply both sides of the inequality by x to simplify: x-5 < 6
•
D. Multiply both sides of the inequality by 6 to simplify: 6x-30 < x

Answer 1

A system of equations is given below.
_ x + 3y = 15
3х + 2y = 10
What is the value of y for the solution to the system? Type your response in the box below.
y=

Answer 2

A linear equation is graphed on the coordinate plane below.
후,,
9+
81
7÷
6T
5T
4+
31
2-
1-
-10 → -8 -7
十
-6
+
+
+
-5
4
-3
| -2
2
9 10
-31
4-
-5
-6
-7-
-8
-9
-101
When graphed on the same coordinate plane, which equation results in a system of equations with exactly one solution?
А. - 2х + 6y = -12
• В. 3х — 9y = 9
С. х - Зу = 6
D. 9x - 3y = 6

Answer 3

Joe claims that the equation y = 2x + b, where b is a real number, represents the graph of a straight line.
Which statement BEST classifies Joe's claim?
A. Joe's claim is true only when bis 0.
• B. Joe's claim is true for all values of b.
C. Joe's claim is not true for any value of b.
• D. Joe's claim is true only when b is not zero.

Answer 4

Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?
A. 40-
-B. 62
C. 841
D. 100

Answer 5

A miniature golf course charges different prices for adults and children. On Saturday, 50 adults and 50 children played, and the golf course earned $800. On Sunday, 65 adults and 75 children played, and the golf course earned $1,100. How much does the golf course charge for adults?
• A. $6
B. $8
C. $10
D. $16

Answer 6

To solve the inequality \( x - 5 < \frac{x}{6} \), the correct first step to simplify the inequality involves eliminating the fraction.

The most straightforward approach is to multiply both sides by 6, which is option D.

So the first step is:
**D. Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \).**

This step will eliminate the fraction on the right side and help to simplify the inequality.

Answer 7

To solve the system of equations:

1. \( x + 3y = 15 \) (Equation 1)
2. \( 3x + 2y = 10 \) (Equation 2)

We can use the substitution or elimination method. Here, I'll use substitution.

From Equation 1, solve for \( x \):
\[
x = 15 - 3y
\]

Now substitute this expression for \( x \) into Equation 2:
\[
3(15 - 3y) + 2y = 10
\]

Distributing the 3:
\[
45 - 9y + 2y = 10
\]

Combine like terms:
\[
45 - 7y = 10
\]

Now, isolate \( y \):
\[
-7y = 10 - 45
\]
\[
-7y = -35
\]

Divide both sides by -7:
\[
y = 5
\]

Thus, the value of \( y \) for the solution to the system is:
\[
y = 5
\]

Answer 8

To determine which equation results in a system of equations with exactly one solution, we need to analyze the slope and y-intercept of the given linear equation and compare it with the options provided.

A system of equations has exactly one solution if the lines represented by the equations intersect at exactly one point, which occurs when the lines are neither parallel (same slope, different intercept) nor the same line (same slope and intercept).

Let’s analyze the given options to find their slopes.

### Given equations to analyze:

1. **\(A. -2x + 6y = -12\)**
Rearranging to slope-intercept form (y = mx + b):
\[
6y = 2x - 12 \implies y = \frac{1}{3}x - 2
\]
(Slope = \(\frac{1}{3}\))

2. **\(B. 3x - 9y = 9\)**
Rearranging:
\[
-9y = -3x + 9 \implies y = \frac{1}{3}x - 1
\]
(Slope = \(\frac{1}{3}\))

3. **\(C. x - 3y = 6\)**
Rearranging:
\[
-3y = -x + 6 \implies y = \frac{1}{3}x + 2
\]
(Slope = \(\frac{1}{3}\))

4. **\(D. 9x - 3y = 6\)**
Rearranging:
\[
-3y = -9x + 6 \implies y = 3x - 2
\]
(Slope = \(3\))

### Summary of Slopes:
- **Option A:** Slope = \(\frac{1}{3}\)
- **Option B:** Slope = \(\frac{1}{3}\)
- **Option C:** Slope = \(\frac{1}{3}\)
- **Option D:** Slope = \(3\)

### Conclusion:
Options A, B, and C have the same slope (\(\frac{1}{3}\)), making them parallel to the original line and resulting in no solution (as they will not intersect). However, option D has a different slope (3), meaning it will intersect with the original line and create exactly one solution.

Thus, the correct answer is:
**D. \(9x - 3y = 6\)**

Answer 9

To classify Joe's claim regarding the equation \( y = 2x + b \):

The equation \( y = mx + b \) is the slope-intercept form of a linear equation, where:
- \( m \) represents the slope of the line,
- \( b \) represents the y-intercept.

In Joe's equation, the slope \( m \) is \( 2 \) (a constant) and \( b \) is any real number that indicates the y-intercept.

Since linear equations in this form are valid for any value of \( b \), they will always represent straight lines.

Therefore, the BEST classification of Joe's claim is:

**B. Joe's claim is true for all values of b.**

Answer 10

Let \( q \) represent the number of quarters and \( d \) represent the number of dimes. We know from the problem:

1. The total number of coins is 124:
\[
q + d = 124 \quad \text{(Equation 1)}
\]

2. The total value in dollars is $25, which can be expressed in terms of cents as 2500 cents. Quarters are worth 25 cents each and dimes are worth 10 cents each:
\[
25q + 10d = 2500 \quad \text{(Equation 2)}
\]

Now we can solve this system of equations.

**Step 1: Solve Equation 1 for \( d \):**
\[
d = 124 - q
\]

**Step 2: Substitute \( d \) in Equation 2:**
\[
25q + 10(124 - q) = 2500
\]

**Step 3: Expand and simplify:**
\[
25q + 1240 - 10q = 2500
\]
\[
15q + 1240 = 2500
\]

**Step 4: Isolate \( q \):**
\[
15q = 2500 - 1240
\]
\[
15q = 1260
\]
\[
q = \frac{1260}{15}
\]
\[
q = 84
\]

So, Xavior had **84 quarters**.

However, the answer choices provided are:
A. 40
B. 62
C. 841
D. 100

None of these choices match our calculation of 84 quarters. It seems there might be an inconsistency, or a miscommunication regarding the options.

If you'd like to double-check or if there's more information or an updated list of choices, please let me know!

Answer 11

To solve for the price that the miniature golf course charges for adults, we can set up a system of equations based on the information provided.

Let:
- \( x \) be the price charged for adults.
- \( y \) be the price charged for children.

From the information provided, we have two scenarios:

1. On Saturday:
\[
50x + 50y = 800 \quad \text{(Equation 1)}
\]

2. On Sunday:
\[
65x + 75y = 1100 \quad \text{(Equation 2)}
\]

**Step 1: Simplify Equation 1**

Divide the entire equation by \( 50 \):
\[
x + y = 16 \quad \text{(Equation 3)}
\]

**Step 2: Simplify Equation 2**

Divide the entire equation by \( 5 \):
\[
13x + 15y = 220 \quad \text{(Equation 4)}
\]

**Step 3: Solve the System of Equations**

Now we can use Equation 3 to express \( y \) in terms of \( x \):
\[
y = 16 - x
\]

**Step 4: Substitute \( y \) into Equation 4:**
\[
13x + 15(16 - x) = 220
\]
Expanding this:
\[
13x + 240 - 15x = 220
\]
Combine like terms:
\[
-2x + 240 = 220
\]
Isolate \( x \):
\[
-2x = 220 - 240
\]
\[
-2x = -20
\]
\[
x = 10
\]

So, the price charged for adults is **$10**.

Thus, the answer is:
**C. $10**