how do you solve this inequality?

Question

-5x + 10 > 70

and this one

-10 > .5 d

Answer 1

-5x + 10 > 70

Subtract 10 from both sides:

-5x > 60

Divide both sides by -5 (which switches the > to a <):

x < -12

-------

-10 > .5d

.5 is 1/2, so multiply both sides by 2:

-20 > .5d(2) = d

Or if you prefer,

d < -20

Answer 2

If you are unsure, simply replace the > sign with an = sign and solve an equality equation. They are basically the same except when using an inequality sign, you have to change the sign when moving a negative to the other side. In the first case: -5x>60, which finishes as x<-12. Any number less than -12 makes the statement true. The next question: -10>0.5d, -10/0.5>d, which finishes as d<-20. In this case the statement will be true for all numbers less than -20. Does that help.

Answer 3

When solving inequalities, the rule to remember is that whenever dividing by a negative number, you must SWITCH the sign.

Take the first inequality. Subtract 10 from both sides:

-5x > 60

Now divide both sides by -5. Since we're dividing by a negative number, the greater-than becomes a less-than:

x < -12

For the second equation, all we need to do to isolate "d" is to divide both sides by 0.5. We're dividing, but it's by a positive number, so the greater-than sign stays as is:

(-10)/0.5 > d

This can be simplified to:

(-10) / (1/2) > d
-10 * 2 > d
-20 > d
d < -20

(In the last step I just rewrote the answer with "d" on the left side. It's just conventional when solving an equation or inequality to put the variable on the left, before the equals or inequality sign.)

Answer 4

An easy way to solve the two inequalities is to move terms and coefficients.

-5x + 10 > 70
equivalent to
10-70 > 5x
equivalent to
-12 > x

-10 > .5 d
equivalent to
-20 > d

Answer 5

-5x+10 > 70
-10 -10
-5x > 60
(-5/-5) (60/-5)
x < -12

-10 > .5 d
-10 (2) > .5 d (2)
-20 > d

Answer 6

1. -5x + 10 > 70
First: subtract 10 from both sides:

-5x + 10 -10 > 70 - 10
-5x > 60

Second: solve for "x" and keep it on one side > divide both sides by -5:

-5x/-5 > 60/-5

Third: when you divide by a negative number, reverse the sign:
x < -12

2. -10 > .5d
*Follow the same format for number 1

Answer 7

1. Rearrange to get -60>5x, so 5x<-60, and divide by 5, which gives x<-12

2. Rewrite as 0.5d<-10 and multiply by 2 to get d<-20

Answer 8

- 5x + 10 > 70

- 5x + 10 - 10 > 70 - 10

- 5x > 60

- 5x / -5 < 60 / - 5

x < - 12

The answer is z < - 12

- - - - - - - - -

- 10 > .5d

- 10 / .5 > .5d / .5

- 20 > d
- - - - - - s-