MATHEMATICS HIGH SCHOOL

Given the equation 7(x + 2) = 2x − 1, solve for the variable. Explain each step and justify your process.Jeff solved a similar equation below. Is Jeff's solution correct? Explain why or why not.
3x − 2 = 5(x + 2)
3x − 2 = 5x + 10
8x = 8
x = 1

Answers

Answer 1
Answer:  
The original equation:                          7(x + 2) = 2x − 1

Eliminate parentheses on the left:        7x + 14 = 2x - 1

Subtract  2x  from each side:                5x + 14 = -1

Subtract  14  from each side:                5x         = -15

Divide each side by  5 :                          x          = -3

==============================

Jeff thought he had solved a similar equation, but his solution is not correct.

Here are his steps, with my commentary:

3x − 2 = 5(x + 2)            The original equation, to be solved.

3x − 2 = 5x + 10            Eliminated parentheses on the right, correctly.

8x = 8                            Subtracted  5x from each side, incorrectly. 
                                      Left side should be  -2x, not  8x .
                
                                     Added  2  to each side, incorrectly.
                                     Right side should be  12, not  8.
                                     
x = 1                           Divided each side by  8, correctly.
                                    But the input from the previous step was garbage,
                                    so the output from this one is garbage.


Jeff should have taken a moment to check his solution,
back in the original equation.

The original equation:            3x − 2 = 5(x + 2)         

If  x = 1, then                       3(1) - 2  =  5 (1 + 2) 

                                               3  -  2  =  5 (3)

                                                     1    =  15            I'm afraid not.
                                                                               Poor Jeff.

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6. The lengths of two sides of a triangle are 5 cm and 8 cm. Between what two measuresshould the length of the third side fall

Answers

Answer:

triangle inequality: the sum of the length of two sides of a triangle must always be greater than the length of the third side.

we know 2 sides whose sum = 5+8 = 13cm

the 3rd side must be <13 included

the length of the third side must be less than 13 cm, i.e. between 1 and 13 (it cannot be equal to 0 because in this case it does not exist)

(answer with "sometimes, always, or never true")
A negative integer is a whole number.

Answers

Answer:

A negative integer is a whole number

NEVER TRUE

Integers run from 0 on up

No decimals

No fractions

Step-by-step explanation:
Always an integer is a whole number :)

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d. 3 and 17

Answers

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Find the measure of each exterior angle for a regular hexagon. Round to the nearest tenth if necessary.

Answers

The measure of each exterior angle for a regular hexagon is 60⁰.

What is Hexagon?

A hexagon is a six-sided polygon or 6-gon. The total of the internal angles of any simple hexagon is 720°.

In a regular Hexagon, all sides are same size and measure of all interior angles are same.

The sum of interior angles of hexagon is (n−2)×180⁰

where n is number of sides of polygon. (6−2)×180⁰ = 720⁰.

here n=6 because hexa means 6

Each interior angle =720⁰/6=120⁰

As we know that the sum of interior and exterior angles is 180⁰

Exterior angle + interior angle =180⁰

Exterior angle +120⁰ = 180⁰

Exterior angle =180⁰−120⁰ = 60⁰

Thus, the measure of each exterior angle for a regular hexagon is 60⁰.

Learn more about Hexagon from:

brainly.com/question/14338151

#SPJ2
Sum of exterior angles: 360 degreesNumber of sides: 6Formula to find the measure of each exterior angle for a regular hexagon:360/n (n=number of sides)So: 360/660So yeah, you are right. The measure of each ext. angle for a regular hexagon is 60 degrees.

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Answers

Solve the following system:

{y = x + 4 | (equation 1)

y + x = 2 | (equation 2)

Express the system in standard form:

{-x + y = 4 | (equation 1)

x + y = 2 | (equation 2)

Add equation 1 to equation 2:

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Multiply equation 1 by -1:

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