i dont know

4/3 x +5 <17

mmm4444bot

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Staff member
Whoops, I accidentally edited this post, when I thought I was appending. :roll:

Edwin_R

New member
umm like this ?
(3) 3/4 x +5 <17
then you would cross out the 3s and then multiply 3 x 5 and multiply 3 x 17, then bring it down and gives you
4 x +15 < 51
-15 < -15
then cross out the 15s and 51 -15 and you get
4x < 36
divide both by 4
4x/4 < 36/4
cross out the 4s on the left and get (x) alone then 36 divided by 4 is 9

so x < 9
Im i right ?

mmm4444bot

Super Moderator
Staff member
Nope. Like this:

??
mmm4444bot said:
The steps to solve this inequality are exactly the same steps we would use to solve the equation.

(1) Subtract 5 from both sides, to isolate the x-term on the lefthand side.

(2) Multiply both sides by 3/4, to solve for x.
(4/3) x + 5 < 17

Subtracting 5 from both sides looks like this:

(4/3) x + 5 - 5 < 17 - 5

Simplify:

(4/3) x < 12

Multiplying both sides by the reciprocal of 4/3 will solve for x:

(3/4)(4/3) x < (3/4)(12)

Simplify:

x < 9

I mean, it's the same result, but I can't follow your logic.

Edwin_R

New member
oh alright thank you, i can still do it my way right ? because you said that i will still get the same answer

can you give me a problem like that and ill solve it please

mmm4444bot

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Staff member
Edwin_R said:
i can still do it my way right ? I'm not sure; I do not understand your reasoning (see below).

because you said that i will still get the same answer No. What I said is that MY result matches yours; I never said that you would get the same.

can you give me a problem like that and ill solve it please Sure. I'll post it below.
You were given the following inequality to solve for x.

4/3 x + 5 < 17

For your first step, you typed the following.

(3) 3/4 x + 5 < 17

Why did you change 4/3 to 3/4 ?

Why did you multiply the lefthand side by 3 without multiplying the righthand side by 3 ?

As I said before, solving a simple inequality like this is exactly the same as solving the corresponding equation. You know how to solve equations, yes?

4/3 x + 5 = 17

Subtract 5 from both sides, then multiply both sides by the reciprocal 3/4.

The only difference, when solving these simple inequalities, is that we must remember the following rule:

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed.

Here's an example why.

-1 is less than 1, right?

-1 < 1

If we multiply both sides by -2 and do NOT reverse the less-than sign, we would have the following.

2 < -2

That inequality is NOT true.

We need to reverse the direction of the inequality symbol, because we multiplied both sides by a negative number.

2 > -2

Here's another example.

100 > 50

You know that's true. Now, divide both sides by -5.

100/(-5) > 50/(-5)

-20 > -10

That result is NOT correct. (-20 is LESS than -10 because -20 lies to the left of -10 on the Real number line, right?)

The result is not correct because I did not reverse the greater-than sign, when dividing both sides by a negative number.

-20 < -10 is true.

Okay, you asked for another inequality to solve, for practice. Here ya go, times two:

$$\displaystyle \frac{3}{8} x \;+\; \frac{7}{8} \;>\; 1$$

and

$$\displaystyle -7 \;-\; (-2x) \;<\; 3$$

Edwin_R

New member
i only got the first one, i put (8) on the left

(8) 3/8 x + 7/8 > 1

cross out all the 8s and then multiply 8 x 7 and 8 x 1 then bring it down

3x 56 > 8

then subtract 56 - 56 and 56 - 8 and you get

3x > -48

divide both by 3 and then you get (x) alone and then 3 divided by -48 you get 16

so my answer is x > 16 im i right ? and i dont even know how to start the other problem

mmm4444bot

Super Moderator
Staff member
Edwin_R said:
i only got the first one, i put (8) on the left

(8) 3/8 x + 7/8 > 1

cross out all the 8s and then multiply 8 x 7 and 8 x 1 then bring it down

3x 56 > 8 This is not correct.
Hi Edwin:

Who taught you the "put 8 on the left" method?

The way I learned is to multiply both sides by 8, and we need to use the Distributive Property to do this multiplication on the lefthand side.

Have you heard of the Distributive Property?

Cheers ~ Mark

Edwin_R

New member
its not put (8) on the left, whatever the denominator is you put the same number on the left, i dont know how to explain it, my teacher taught me

mmm4444bot

Super Moderator
Staff member
Fair enough.

The issue is that when you cancel the denominators, the 8 gets canceled, too. After these cancellations, there is no 8 left to multiply times 7 to get 56.

$$\displaystyle \frac{3}{8} x \;+\; \frac{7}{8} \;>\; 1$$

We want to multiply both sides of the inequality by 8 (to get rid of the fractions). Here is how I write it.

$$\displaystyle 8 \left ( \frac{3}{8} x \;+\; \frac{7}{8} \right ) \;>\; 8 (1)$$

I used parentheses to show that the entire lefthand side gets multiplied by 8.

We use the Distributive Property to do this multiplication. Here is how I write it.

$$\displaystyle (8) \left ( \frac{3}{8} x \right ) \;+\; (8) \left ( \frac{7}{8} \right ) \;>\; 8$$

On the lefthand side, all of the 8s cancel, right? That leaves us with the following.

$$\displaystyle 3x \;+\; 7 > 8$$

Do you understand the Distributive Property, and why we have a 7 instead of a 56 ?

If you understand, then try to finish solving for x.

If you do not understand something, please tell me.

Edwin_R

New member
oh i get it now, okay you have

3x + 7 > 8
-7 -7

and then you get

3x > 1 divide both by 3 and you get x > 3 I'm i right?

NO! x > 1/3

huh ?

Edwin_R

New member
dont scream please and thank you

mmm4444bot

Super Moderator
Staff member
1 divided by 3 is not 3.

1 divided by 3 is 1/3.

$$\displaystyle 3x \;>\; 1$$

Divide both sides by 3.

$$\displaystyle \frac{3x}{3} \;>\; \frac{1}{3}$$

The 3s cancel, on the lefthand side.

$$\displaystyle x \;>\; \frac{1}{3}$$

Edwin_R

New member
oh yeah thats right

mmm4444bot

Super Moderator
Staff member
mmm4444bot said:
$$\displaystyle -7 \;-\; (-2x) \;<\; 3$$
In the example above, the expression -2x is being subtracted.

Do you know the rule for subtracting a negative?

Edwin_R

New member
oh yeah thats right

mmm4444bot

Super Moderator
Staff member
Edwin_R said:
oh yeah thats right