Solve the given inequality and graph the solution on a number line -x/2 + 3/2 + < 5/2 .

Mathematics

2 answers:

liq [111]3 years ago

5 0

Answers in Image attached

Hope this helps

irina [24]3 years ago

5 0

Well, in that case, here goes...

The first thing I'd do is clear the fractions- that is, I'd multiply each of them by 2 because 2 is the lowest common denominator.

That leaves you with -x + 3 < 5
Now solving isn't too bad...

-x + 3 - 3 < 5 - 3 (subtract 3 from both sides)
-x < 2

The x isn't alone! That - is hanging on...so multiply both sides by -1 to get rid of it!

-x * -1 < 2 * -1 WAIT! We multiplied by a negative!!
-x * -1 > 2 * -1 Had to flip that inequality ofver!

x > -2

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which equation represents a line that is parallel to the line whose equation is 3x-2y=7; which equation represents a line parall

aleksley [76]

The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.

How are parallel straight lines related?

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

We have been given a parallel line with has equation

3x-2y=7

In order to solve this, the slope of the original line.

3x - 2y = 7

-2y = -3x + 7

y = 3/2x - 7/2

thus its slope is 3/2.

thus, the slope of the needed line is 3/2 too.

we know that any line that is parallel to that would have this slope.

So anything is written in the form:

y = 3/2x + b

The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.