Question

Plz help due today

Explain why x = 5 makes 4x − 1 ≤ 19 true but not 4x − 1 < 19.

Part B: What value from the set {6, 7, 8, 9, 10} makes the equation 5x + 2 = 47 true? Show your work.

Answer 1

Part A

Explanation:

4x − 1 ≤ 19 is the same as

4 times 5 minus 1 = 19

So 19 ≤ 19

The symbol ≤ means that the number on the left of the sign is smaller OR EQUAL TO the number on the right

19 is not smaller than 19 but is equal to 19

The symbol < means only that the number on the left is smaller than the number on the right

Part B

Answer:

9

Explanation:

5x + 2 = 47

We need the x ( which is the unknown number) to be by its self on one side of the equation ( or the equal sign)

The equation expanded is:

5 * x + 2 = 47 (the symbol * is the times symbol)

Firs we can move the 2 to the other side by taking away the two from the left of the equation and moving it to the right

5x + 2 = 47

-2 -2

To take away the two on the left of the equation we do 2-2 which is 0. And whatever we do on one side of the equation we have to do on the other so 47-2 which is 45

Now the equation looks like:

5x = 45

Now remember that 5x is actually 5 times x

So

5 * x = 45

Now we need to have only x on the left side so we need to move the 5 to the right

To do this we have to make * 5 turn into 0

The opposite of times is divide so we divid the 5 by 5

5/5= 0

Now we do the same on the other side of the equation

5x = 45

5x/5 = 45/5

x = 9

So now x is by its self we can see x = 9

So the answer is

9

Answer 2

[PART A]

We will input x = 5 into both inequalities and solve for x by isolating the variable.

4x − 1 ≤ 19

4(5) − 1 ≤ 19

20 − 1 ≤ 19

19 ≤ 19

➜ This is true because the inequality states that 19 is less than or equal to 19. 19 = 19, so this is true.

4x − 1 < 19

4(5) - 1 < 19

20 - 1 < 19

19 < 19

➜ This isn't true because the inequality states that 19 is less than 19. We do now have the equal to part here, and 19 is not less than 19. This is why it isn't true.

[PART B]

We will solve for x in the given equation and see which value from the set is correct. You can also substitute each value from the set into the equation until you find the correct answer, but this method is quicker and less prone to errors.

Given:

5x + 2 = 47

Subtract 2 from both sides of the equation:

5x = 45

Divide both sides of the equation by 5:

x = 8

Part B Answer: 8