can you help solve this equation?

Question

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

Answer 1

Solving inequality is very like solving equation. The only difference: if divide or multiply both sides of inequality by negative number, we have to change sign of inequality to opposite.
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- 2x + 4 > 5(x - 2)

- 2x + 4 > 5x - 10
       - 4          - 4

- 2x  >  5x - 14
- 5x    - 5x

 - 7x    >   - 14
÷(- 7)      ÷(-7)

  x < 2 , or all numbers out of interval (- ∞, 2) 

Answer 2

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

There are two ways to solve the equation. It all depends on how you go about it. Both ways are correct and both ways get you the same answer. The first step to both is expanding 5(x-2). Just multiply 5 by x and by 2.

-2x+4>5x-10

Here is where you can go one of two ways. You can either add 2x to both sides or subtract 5x from both sides. if I can help it, I prefer to keep x positive at all times. A positive x will always be your end goal, so if you can keep it positive it makes the equation easier. So here, I added 2x to both sides and I added 10 to both sides.

14>7x

Then you divide both sides by 7 and you get your final answer.

2>x or x<2. 

The second way to do it is not my favorite method, because you keep you x negative when you could make it positive and it can make the problem more difficult but it can be done.

-2x+4>5x-10

You know subtract 5x from both sides and subtract 4 from both sides.

-7x>-14

Now here is where it can get tricky. You divide by -7 from both sides. But when you divide or multiply by a negative, you flip the inequality sign.  

x<2

Both methods give you the same answer. It is important to know how to solve an inequality in both the orange and the green method. It is important to know how to solve an inequality with the green method and everything about negative inequalities. But in my opinion, keeping x positive is a lot easier to work with than a negative x.

Answer 3

PEMDAS Basic rules: 

Step 1. Complete the right side of the equation to get rid of the parentheses...in this case multiply the coefficient outside the parenthesis to 5x - 10...inserting the calculated binomial...

Rewrite the equation to be:   -2x + 4 > 5x - 10

Step 2. Look at your equation...combine like terms...remember...it easiest to keep the variable...(in this case...X...a positive value.) Key: we're done with the P, the E, the D(at this point), and the M...all that's left is the A and the S. Add the negative variable on the left side of the equation with its positive opposite to get zero. What one does on the left side of the inequality sign...you HAVE to do the same on the right side. Now you have a positive variable which has a coefficient of 7 and a variable x. there are two constants, so do the same, since they are like terms. 

Step 3. With addition, you now have all the constants on one side and the variables on the other side of the inequality sign.  Last thing to do is eliminate the coefficient from the variable, in this case, by division, to leave the variable x. 

Rewrite the equation(which you now have):   4 + 10 > 7x    or     14 ÷ 7 > x

NOTE: you should know when to invert the inequality sign...there are rules for that...

I'll show you how to answer these kinds of questions...work on doing more. It would do you no good if I just gave you the answer.

Good luck.    ;  )

Answer 4

Dayana,

Try by expanding the right side of the inequality (multiplying the 5 times the x and the 2).  Next get all the "x" terms on one side of the inequality sign and the "numbers" on the other.  Be careful when you do this because there is something in your math text book about when to reverse the inequality sign - check it out.  When you get x by itself on one side and numbers on the other - you solved it!  Don't forget to try your answer back in the original inequality to make sue you didn't make a multiplication or division error.  Take your time and work through the problems systematically.  It works.

 

Thanks,

Chris

 

 

Answer 5

-2x+4>5x-10

-7x> -14

flip left and right sides

14>7x

2>x

x<2