SOLUTION: I cannot figure out how to do these two problems, I have tried it many different ways and cannot get the right answer. Help me! 1) |2(4-4x)+4|=3 and 2) |9-7x| is less than 7.

Algebra ->  Absolute-value -> SOLUTION: I cannot figure out how to do these two problems, I have tried it many different ways and cannot get the right answer. Help me! 1) |2(4-4x)+4|=3 and 2) |9-7x| is less than 7.       Log On


   

Question 24132: I cannot figure out how to do these two problems, I have tried it many different ways and cannot get the right answer. Help me! 1) |2(4-4x)+4|=3 and
2) |9-7x| is less than 7.
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!

I didn't learn how to solve these until university would you believe! They couldn't be easier once you know how to deal with them though.


As I'm sure you know, the absolute value function gives you back it's argument without the sign. So if abs%28x%29=5 then either x=5 or -x=5. Applying the same idea to your question 1, we get two equations:


2%284-4x%29%2B4=3

and


-2%284-4x%29-4=3

Using the super automatic equation solver thingy, we get:


Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=1.125.
  • Graphical form: Equation 2%2A%284-4x%29%2B4=3 was fully solved.
  • Text form: 2*(4-4x)+4=3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%284-4x%29%2B4=3+%29
    For tutors: simplify_cartoon( 2*(4-4x)+4=3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%28highlight_red%28+4+%29-4%2Ax%29%2B4=3.
Moved 4 to the right of expression
It becomes 2%2A%28-4%2Ax%2Bhighlight_green%28+4+%29%29%2B4=3.
Look at 2%2A%28-4%2Ax%2B4%29%2B4=highlight_red%28+3+%29.
Moved these terms to the left highlight_green%28+-3+%29
It becomes 2%2A%28-4%2Ax%2B4%29%2B4-highlight_green%28+3+%29=0.
Look at 2%2A%28-4%2Ax%2B4%29%2Bhighlight_red%28+4+%29-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes 2%2A%28-4%2Ax%2B4%29%2Bhighlight_green%28+1+%29=0.
Look at highlight_red%28+2%2A%28-4%2Ax%2B4%29+%29%2B1=0.
Expanded term 2 by using associative property on %28-4%2Ax%2B4%29
It becomes -highlight_green%28+2%2A4%2Ax+%29%2Bhighlight_green%28+2%2A4+%29%2B1=0.
Look at -highlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2Ax%2B2%2A4%2B1=0.
Multiplied numerator integers
It becomes -highlight_green%28+8+%29%2Ax%2B2%2A4%2B1=0.
Look at -8%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2B1=0.
Multiplied numerator integers
It becomes -8%2Ax%2Bhighlight_green%28+8+%29%2B1=0.
Look at -8%2Ax%2Bhighlight_red%28+8+%29%2Bhighlight_red%28+1+%29=0.
Added fractions or integers together
It becomes -8%2Ax%2Bhighlight_green%28+9+%29=0.
Look at highlight_red%28+-8%2Ax%2B9+%29=0.
Solved linear equation highlight_red%28+-8%2Ax%2B9=0+%29 equivalent to -8*x+9 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=1.125.

Universal Simplifier and Solver


Done!


and


Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=1.875.
  • Graphical form: Equation -2%2A%284-4x%29-4=3 was fully solved.
  • Text form: -2*(4-4x)-4=3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-2%2A%284-4x%29-4=3+%29
    For tutors: simplify_cartoon( -2*(4-4x)-4=3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -2%2A%28highlight_red%28+4+%29-4%2Ax%29-4=3.
Moved 4 to the right of expression
It becomes -2%2A%28-4%2Ax%2Bhighlight_green%28+4+%29%29-4=3.
Look at -2%2A%28-4%2Ax%2B4%29-4=highlight_red%28+3+%29.
Moved these terms to the left highlight_green%28+-3+%29
It becomes -2%2A%28-4%2Ax%2B4%29-4-highlight_green%28+3+%29=0.
Look at -2%2A%28-4%2Ax%2B4%29-highlight_red%28+4+%29-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes -2%2A%28-4%2Ax%2B4%29%2Bhighlight_green%28+-7+%29=0.
Look at -2%2A%28-4%2Ax%2B4%29%2Bhighlight_red%28+-7+%29=0.
Removed extra sign in front of -7
It becomes -2%2A%28-4%2Ax%2B4%29-highlight_green%28+7+%29=0.
Look at -highlight_red%28+2%2A%28-4%2Ax%2B4%29+%29-7=0.
Expanded term -2 by using associative property on %28-4%2Ax%2B4%29
It becomes highlight_green%28+2%2A4%2Ax+%29-highlight_green%28+2%2A4+%29-7=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2Ax-2%2A4-7=0.
Multiplied numerator integers
It becomes highlight_green%28+8+%29%2Ax-2%2A4-7=0.
Look at 8%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+4+%29-7=0.
Multiplied numerator integers
It becomes 8%2Ax-highlight_green%28+8+%29-7=0.
Look at 8%2Ax-highlight_red%28+8+%29-highlight_red%28+7+%29=0.
Added fractions or integers together
It becomes 8%2Ax%2Bhighlight_green%28+-15+%29=0.
Look at 8%2Ax%2Bhighlight_red%28+-15+%29=0.
Removed extra sign in front of -15
It becomes 8%2Ax-highlight_green%28+15+%29=0.
Look at highlight_red%28+8%2Ax-15+%29=0.
Solved linear equation highlight_red%28+8%2Ax-15=0+%29 equivalent to 8*x-15 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=1.875.

Universal Simplifier and Solver


Done!


Don't forget to put your answers back in to check!


Now you know how to do the first problem, have another go at the second one again yourself, but don't forget the really imporant rule:


When you multiply an inequality by a negative number you must reverse the sign.


I've forgotton to do that far too many times


Hope that helps


Kev