If you were to graph the inequality 35<7x

Question

on a number line:(2 points)
Would you use an open or closed circle? [response area]

Would your arrow on the number line point to the left or to the right? [response area]

1st responses
open
closed

2nd responses
left
right

Answer 1

1st response: open
2nd response: right

Explanation:

• Since the inequality is "35 < 7x," it indicates that 7x is greater than 35. When graphing this on a number line, the open circle is used for the value 5 (since \(x > 5\)), indicating that 5 is not included in the solution.
• The arrow points to the right, indicating that all values greater than 5 satisfy the inequality.

Answer 2

Match the inequality to its graphed solution.(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

Answer 3

It looks like you're looking for a way to match inequalities to their graphed solutions. However, since I cannot see the available inequalities or graphs, I can provide a general guide on how to match them.

Steps to Match Inequalities to Their Graphs:

1. Identify the Inequality: Look at the inequality you have. It can be in forms like:

   • \( x < a \) (open circle at a, shading left)
   • \( x \leq a \) (closed circle at a, shading left)
   • \( x > a \) (open circle at a, shading right)
   • \( x \geq a \) (closed circle at a, shading right)
   • \( ax < b \) or similar transformations.

2. Analyze the Graph: Check the number line or graphical representation:

   • Open circles mean the value is not included (e.g., \( < \) or \( > \)).
   • Closed circles mean the value is included (e.g., \( \leq \) or \( \geq \)).
   • Arrows that point left indicate values less than a certain point, while arrows that point right indicate values greater.

3. Match Accordingly: Based on the above analysis, find the appropriate inequality that corresponds to the graph.

If you can provide specific inequalities or descriptions of the graphs, I’d be glad to help you match them accurately!

Answer 4

17. Solve the equation filling in the steps: 2(x−3)+21=−3
(6 points)
Distribute to get [Response area]

Combine like terms to get [Response area]

Use the (choose a property) [Response area] to get (resulting equation) [Response area]

Use the (choose a property) [Response area] to get (resulting answer) [Response area]

responses
2x - 3 +21 = -3
x = -9
2x + 18 = -3
multiplication property of equality
x = 24
2x + 15 = -3
x = -21/2
2x - 6 + 21 = -3
subtraction property of equality
addition property of equality
division property of equality
-1x = -24
2x = -18
2x = -21

Answer 5

Let’s solve the equation step-by-step, filling in the required responses.

Given equation:
\[ 2(x - 3) + 21 = -3 \]

Step 1: Distribute

Distribute to get:
\[ 2x - 6 + 21 = -3 \]
(This matches with the response option: \( 2x - 6 + 21 = -3 \))

Step 2: Combine like terms

Combine like terms to get:
\[ 2x + 15 = -3 \]
(This matches with the response option: \( 2x + 15 = -3 \))

Step 3: Use the addition property of equality

Use the (choose a property):
\[ \text{Subtraction property of equality} \]
to get:
\[ 2x + 15 - 15 = -3 - 15 \]
which simplifies to
\[ 2x = -18 \]

Step 4: Use the division property of equality

Use the (choose a property):
\[ \text{Division property of equality} \]
to get:
\[ x = -9 \]
(This matches with the response option: \( x = -9 \))

Summary of Responses:

1. Distribute to get: \( 2x - 6 + 21 = -3 \)
2. Combine like terms to get: \( 2x + 15 = -3 \)
3. Use the: Subtraction property of equality
   to get: \( 2x = -18 \)
4. Use the: Division property of equality
   to get: \( x = -9 \)

These steps correctly solve the equation \( 2(x - 3) + 21 = -3 \) and match the response options provided.

Answer 6

Solve the following:(2 points)
ax−44<15
ax+15=44
responses
x = 29a
x = 59/a
x < 59/a
x = 29/a
x < 29/a
x < 29a
x = 59a

Answer 7

Let's solve each of the given equations one at a time.

1. Inequality: \( ax - 44 < 15 \)

Step 1: Add \( 44 \) to both sides.

\[ ax < 15 + 44 \] \[ ax < 59 \]

Step 2: Divide by \( a \) (assuming \( a \neq 0 \)).

\[ x < \frac{59}{a} \]

Final Step for the Inequality:

Thus, the solution for \( ax - 44 < 15 \) is:

Response: \( x < \frac{59}{a} \)

---

2. Equation: \( ax + 15 = 44 \)

Step 1: Subtract \( 15 \) from both sides.

\[ ax = 44 - 15 \] \[ ax = 29 \]

Step 2: Divide by \( a \) (assuming \( a \neq 0 \)).

\[ x = \frac{29}{a} \]

Final Step for the Equation:

Thus, the solution for \( ax + 15 = 44 \) is:

Response: \( x = \frac{29}{a} \)

---

Summary of Responses:

1. From the inequality \( ax - 44 < 15 \): Answer: \( x < \frac{59}{a} \)
2. From the equation \( ax + 15 = 44 \): Answer: \( x = \frac{29}{a} \)

These steps yield the correct responses based on the provided equations and inequalities.

Answer 8

The base of a triangle is four less than three times the height. The area of the triangle is 38 square centimeters. A=(b×h)2
(3 points)
An expression for the base of the triangle: [Response area]

Equation for the area of the triangle, substituting in for the base: [Response area]

The first step in solving for h: [response area]

responses
divide both sides by h
4 - 3h
3h - 4
38 = [3h - 4 x h] / 2
multiply both sides by 2
4h - 3
3h - 4 = 1/2 [38 x h

Answer 9

To solve the problem step-by-step, we can fill in each part based on the information provided.

Given Information:

• The base of the triangle is four less than three times the height.
• Area of the triangle is 38 square centimeters.
• The formula for the area of the triangle is \( A = \frac{b \times h}{2} \).

Step 1: Expression for the base of the triangle

Let \( h \) represent the height of the triangle. Then, the expression for the base \( b \) can be given as: \[ b = 3h - 4 \]

Response: \( 3h - 4 \)

---

Step 2: Equation for the area of the triangle, substituting in for the base

Now substituting the base \( b \) into the area formula gives us: \[ 38 = \frac{(3h - 4) \times h}{2} \]

To simplify, we can write it directly as: \[ 38 = \frac{(3h - 4)h}{2} \]

Response: \( 38 = \frac{(3h - 4) \times h}{2} \)

---

Step 3: The first step in solving for \( h \)

To eliminate the fraction, the first step in solving for \( h \) would be to multiply both sides by \( 2 \): \[ 76 = (3h - 4)h \]

This means the first action we take to solve the equation is: Response: \( \text{multiply both sides by 2} \)

---

Summary of Responses:

1. An expression for the base of the triangle: \( 3h - 4 \)
2. Equation for the area of the triangle, substituting in for the base: \( 38 = \frac{(3h - 4) \times h}{2} \)
3. The first step in solving for \( h \): \( \text{multiply both sides by 2} \)

These completed steps accurately reflect the reasoning behind the problem!

Answer 10

Solve the equation for y: 3x+5y=60
(1 point)
Responses

y=57x5
y is equal to 57 x over 5

y=60−3x
y is equal to 60 minus 3 x

y=60+3x5
y is equal to 60 plus 3 x over 5

y=−35x+12

Answer 11

To solve the equation \(3x + 5y = 60\) for \(y\), we can follow these steps:

Step 1: Isolate \(5y\)

We start with the original equation:

\[ 3x + 5y = 60 \]

Subtract \(3x\) from both sides:

\[ 5y = 60 - 3x \]

Step 2: Solve for \(y\)

Now, divide both sides by \(5\):

\[ y = \frac{60 - 3x}{5} \]

This can be rewritten as:

\[ y = 12 - \frac{3}{5}x \]

Summary:

From the options provided:

• Response: \( y = 60 - 3x \)

However, none of the choices directly match the simplified solution as it is not expressed in terms of dividing \(60 - 3x\) by \(5\).

The closest option, related to isolating \(y\), would be:

• \( y \text{ is equal to } 60 - 3x \)

But for clarity and correctness, this is the solution we derived: \[ y = 12 - \frac{3}{5}x \]

However, based on your options, the most appropriate response for isolating \(y\) would be:

• y = 60 - 3x (if we consider that as the primary expression before division for 5).

Let me know if there is anything more specific you need!