inequality?

Question

solve for x and how did you get to the answer

3x-7>5

and another equation

(4 + x) / 5< or equal to 8

Answer 1

1) Add 7 to each side of the inequality:

3x > 12

Now divide by 3 on each side:

x > 4


2)First, multiply each side by 5:

4+x <= 40

Now, subtract 4 from each side:

x < or = 36

Answer 2

I believe the first answer is
x>4
and the second is
(4+x)< or equal to 40

First, for 3x-7>5
you have to isolate the 3x, so you add 7 to cancel 3x-7 out. And what you do to one side of the equal sign (in this case, the greater than sign), you must do to the other. So you also have to add 7 to the 5. So now, you have 3x>5+7, becoming 3x>12. Again, you have to isolate, this time, the x only. Actually, 3x is 3 times x. So you do an inverse operation. 3x/3=x. Now you have to divide by 3 on the other side too. Because remember; you have to do the same operation to both sides. So 12/3 is 4; hence x>4.

Now, (4+x)/5 (4+x)/5 Get (4+x)/5 isolated; multiply by 5
Now you have (4+x)
But you have to multiply the other side by 5 also; 8*5=40
(4+x)< or equal to 40
Order of operations (PEMDAS) says you must do the parenthesas first, but since you don't know what x is, it's okay to leave it like that. Ta-Dah! Hope that helped.

Answer 3

Greetings,

Solving inequalities are just like solving equations...so

3x - 7 > 5, first isolate the 3x term by ADDING +7 to both sides of the inequality, which gives you

3x > 12

now solve for x by dividing both sides by 3 giving you,

x > 4

The second question is pretty much the same thing...

(4+x)/5 <= (the sign for less than or equal to) 8

first remove the fraction by multiplying both sides by 5 which gives you

(4+x) <= 40

isolate x by substracting 4 from both sides...

x <= 36

Hope this helps.

Cheers,
Mark

Answer 4

Just treat the inequality like an equation, getting x on one side:
3x - 7 > 5
3x > 5 + 7
3x > 12
x > 4

(4+x)/5 <= 8
4+x <= 40
x <= 36

The only special rule you need to know for simplifying inequalities is that if you multiply or divide both sides by a negative number, you have to change the direction of the inequality sign. But we didn't even have to do that here.

Answer 5

(Ignore the greater and less signs. The only time it affects the answer for these problems is if you divide the answer by a negative problem. That means the greater sign changes to the less than and the less than to the greater)

You want to get the term out.
Then you get x alone by dividing.

1. Add 7 to both sides:

3x-7>5 to 3x>12

Divide by 3:

3x>12 to x>4

2. Multiply by 5 on both sides:

(4 + x) / 5`<= 8 to 4 + x <= 40

Subtract by four:

4 + x <= 40 to x <= 36

Answer 6

Solve these just like you would if the < or > was an =. But there is one extra rule: if you multiply or divide by a negative number, you must flip the sign.

3x - 7 > 5
Add 7 to both sides.
3x > 12
Divide by 3 on both sides.
x > 4
There you go.

(4 + x)/5 <= 8
Multiply by 5 on both sides.
4 + x <= 40
Subtract 4 from both sides.
x is less than or equal to 36.

Answer 7

3x -7 > 5 add 7 to both sides
3x > 12 divide by 3 both sides
x > 4

(4+x)/5 <= 8 multiply both sides by 5
4+x <= 40 subtract both sides by 4

x <= 36

Answer 8

3x - 7 > 5
3x > 5 + 7
x > 4

Answer 9

3X-7 >5 "move 7 to other side and change sign"
3X >12 (÷3)
x > 4
S.S={x belong to R : x>4}
(4+x)/5 4+x < or = 40 "move 4 to other side and change sign"
X < or = 36
S.S={x belong to R : x < or = 36}

Answer 10

3x-7>5
3x>12
x>4

(4+x)/5<= 8
4+x<=40
x<=36