Algebra help! Inequalities.?

Question

5 (x + 4) - 2 (x +6) > 5 (x + 1)

ok and the sign is not just greater than, it's equal to or greater than, i just didn't know how to make it on the computer!!

Please help...
or if you know how to work them on a graphing calculator w/ out any programs.. tell me!

Thankss!!!!

Answer 1

You can solve an inequality just like an equation; just remember that if you multiply or divide by something negative, you have to flip the ">" or "<".

I will use '>=' to denote 'greater than or equal to.'

5 (x + 4) - 2 (x + 6) >= 5 (x + 1)

First clear the parentheses:

5x + 20 - 2x - 12 >= 5x + 5

Then combine like terms:

3x + 8 >= 5x + 5

Now subtract 3x from both sides:

8 >= 2x + 5

Now subtract 5 from both sides:

3 >= 2x

Now divide by 2:

3/2 >= x

This is equivalent to

x <= 3/2.

So the solution is all x less than or equal to 3/2.

Answer 2

5 (x + 4) - 2 (x +6) ≥ 5 (x + 1)

First, by applying the distributive property of multiplication over addition a(b+c)=ab+ac to the left side of the inequality, we get
5x + 20 + (-2x) + (-2)(6) = 5x + 20 +(-2x) + (-12)

NOTE: adding equalities to both sides doesn't change the inequality. But if you multiply by a factor of -1, it flips the inequality, i.e., < becomes >, or > becomes < or ≤ becomes ≥, or ≥ becomes ≤.

Now, by applying the associative property of addition (a+b)+c=a+(b+c), and the commutative property of addition a+b=b+a we get
5x + (-2x) + 20 + (-12) = 5x + (-2x) + 8

And applying the distributive property again we get
(5 + (-2))x + 20 = 3x + 20… on the left side

The right side = 5x + 5, applying the distributive property.

So we have
3x + 20 ≥ 5x + 5
Adding -5 to both sides,
3x + 15 ≥ 5x

Adding -3x to both sides
15 ≥ 2x

Multiplying both sides by ½,
15/2 ≥ x

More traditionally…
x ≤ 15/2

And, to get symbols… some of them, do you work in Word. Use the Insert/Symbol option… you can get stuff like ≥, ≤, ±, √, etc.

To see what it looks like, get a piece of graph paper. Mark off the x and y axes. Go out the x Axis to x= 15/2 (7.5). Draw a vertical line through that point. That line represents all the points that satisfy x = 15/2. All the points are ≤ 15/2

Now look at a point to the right of the line… say x=10. is 10 ≤ 15/2? Ok, so the solution does not include points to the right of the line.

Look at a point to the left of the line… say x = 0. Is 0 ≤ 15/2? Ok so all the solution to the inequality includes all the points to the left of the line.

Therefore, the solution includes the vertical line and all the points to the left of it.

If you’re graphing in a plane, the value of y doesn’t make any difference. If you’re graphing on the number line, y = 0.

Answer 3

5x + 20 - 2x - 12 ≥ 5x + 5
3x + 8 ≥ 5x + 5
3 ≥ 2x
x ≤ 3 / 2

Answer 4

5 (x + 4) - 2 (x +6) ≥ 5 (x + 1)
5x + 20 - 2x - 12 ≥ 5x + 5
-2x + 8 ≥ 5
-2x ≤ 5 - 8
x ≤ -3/-2
x ≤ 1.5
Solution: {x belongs to R| x ≤ 1.5}
>::<

Answer 5

5x+20-2x-12>=5x+5

3x+8>=5x+5
3x-3x+8>=5x-3x+5
8>=2x+5
8-5>=2x
3>=2x
3/2>=x
2/3<=x
2/