Question

# Solve 3.5x+19≥1.5x-7

Hint:

### Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

## The correct answer is: x≥-13

### Step 1 of 1:

Rearrange and solve the inequality,

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

### Related Questions to study

### Determine whether each graph represents a function ?

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

### Determine whether each graph represents a function ?

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

### Choose the negative adjectives starting with ' u '

Explanation-Negative adjectives are the word that explains / pronounce negatively.

### Choose the negative adjectives starting with ' u '

Explanation-Negative adjectives are the word that explains / pronounce negatively.

### Describe the possible values of x.

- Step-by-step explanation:

- Given:

a = x + 11, b = 2x + 10, and c = 5x - 9.

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

x + 11 < 7x + 1,

11 – 1 < 7x - x

10 < 6x

< x,

1.6 < x

Now, consider,

3x - 19 < x + 11

3x - x < 11 + 19

2x < 30

x < ,

x < 15

therefore,

1.6 < x < 15

- Final Answer:

### Describe the possible values of x.

- Step-by-step explanation:

- Given:

a = x + 11, b = 2x + 10, and c = 5x - 9.

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

x + 11 < 7x + 1,

11 – 1 < 7x - x

10 < 6x

< x,

1.6 < x

Now, consider,

3x - 19 < x + 11

3x - x < 11 + 19

2x < 30

x < ,

x < 15

therefore,

1.6 < x < 15

- Final Answer:

### Write the solutions to the given equation.

Rewrite them as the linear-quadratic system of equations and graph them to solve.

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is

Re arranging them, we have:

Step 2 of 2:

Graph the quadratic equation:

The solution is .

Note:

A quadratic equation can be solved using different identities and even simplifying them.

### Write the solutions to the given equation.

Rewrite them as the linear-quadratic system of equations and graph them to solve.

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is

Re arranging them, we have:

Step 2 of 2:

Graph the quadratic equation:

The solution is .

Note:

A quadratic equation can be solved using different identities and even simplifying them.

### Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.

5 inches, 12 inches

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- while finding possible lengths of third side use below formula

- Step-by-step explanation:

- Given:

a = 5 inches, b = 12 inches.

- Step 1:
- Find length of third side.

c < a + b

∴ c < 5 + 12

c < 17

- Step 2:

b – a < c < a + b

12 – 5 < c < 5 + 12

7 < c < 17

Hence, all numbers between 7 and 17 will be the length of third side.

- Final Answer:

### Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.

5 inches, 12 inches

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- while finding possible lengths of third side use below formula

- Step-by-step explanation:

- Given:

a = 5 inches, b = 12 inches.

- Step 1:
- Find length of third side.

c < a + b

∴ c < 5 + 12

c < 17

- Step 2:

b – a < c < a + b

12 – 5 < c < 5 + 12

7 < c < 17

Hence, all numbers between 7 and 17 will be the length of third side.

- Final Answer:

### Identify the common noun in the given sentence

"The mice are afraid of a cat"

Explanation-Mice Words which are used as names of persons, animals, places or things a