7-4x is less than or equal to 2-3x explain and please help me.?

Answer 1

7 - 4x <= 2 - 3x
7 - 4x + 4x <= 2 - 3x + 4x
7 - 2 <= 2 - 2 + x
5 <= x

draw a solid line representing x = 5 [through points (5,0) and (5,1)] it would be dashed if the inequality were strictly < and not equal.

then shade all of the area that makes the inequality true (the side that doesn't include the origin).

Answer 2

Put numbers in place of x and see what you get.
If x=1
Then 7-4(1) = 7-4 = 3 and 2-3(1) = 2-3 = -1

If x=2
Then 7-4(2) = 7-8 = -1 and 2-3(2) = 2-6 = -4

So you can see by placing numbers in place of x that 2-3x will always have a smaller value than 7-4x. So based on how you worded your question, 7-4x is neither less than nor equal to 2-3x. Rather, 7-4x is greater than 2-3x.

Answer 3

This is an inequality equation. You can use algebra the same as with a normal equation that uses a = sign. It is just that the solution for x will likely be a range of numbers rather than just one number.

7 - 4x <= 2 - 3x
-4x <= -5 - 3x
-x <= -5
x <= 5

The solution then is that x is lesser than or greater than 5. You can also graph this on the number line:

<========O
<=|=|=|=|=|=|=|=>
....0 1 2 3 4 5

x = {... -2, -1, 0, 1, 2, 3, 4, 5}

Over the number that is specified as the range, if it is included in the solution set, you would place a filled-in circle over the number. You put an open circle over the number only if it is not included (i.e. the solution was x < 5). I can't fill in the hole due to the limitations of the keyboard so please imagine that the circle is filled in for this number line graph of the solution set. The bracketed range of numbers that I specify for x is another way to state the solution set with the ellipsis to denote the infinite range.

Answer 4

Okay, lets say that X is 5.
7-4(X)= 7-4(5)
7-20= -13

2-3(X)= 2-3(5)
2-15= -13

Both equal -13 so that would make them equal.

Since we don't know what X equals, this problem could be true.

Answer 5

Lets say x=1
7-4(1)= 3
2-3(1)= -1

x=2
7-4(2)= -1
2-3(2)= -4

so 7-4x > 2-3x

7-4x is always greater than 2-3x

Answer 6

Depends. 7 - 4x <_ 2 - 3x iff 5 <_ x, or x >_ 5.

Show my work.