4x + 3 > 2(x - 3) on a number line.
2007-01-02 20:21:30 · 13 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The problem is simple: it's an inequation, and the goal is to find the values of x that satisfy the inequation, e.g. the values of x such that:
4x + 3 > 2(x - 3)
The usual procedure is to work as if there was an "=" at the middle, and try to isolate the x (as you do usually with equations). Let's do it step by step.
4x + 3 > 2(x - 3)
so:
4x + 3 > 2x - 6 [because 2(x - 3) = 2x - 6]
so:
4x + 3 - 2x > - 6 [I passed the "x" term to the left)
so:
4x - 2x > -3 - 6 [I passed the "3" number to the right]
so:
2x > -9 [because 4x - 2x = 2x; and -3 - 6 = -9]
so:
x > -9/2 [I passed the number 2 to the right, dividing]
And this is the answer:
When x > -9/2, then the equation 4x + 3 > 2(x - 3) is satisfied
If you have any question, feel free to contact me!
2007-01-02 21:41:15 · answer #1 · answered by bartacuba 2 · 2⤊ 1⤋
First: use distribution > multiply 2 with everything in the parenthesis >
= 4x + 3 > 2(x) - 2(3)
= 4x + 3 > 2x - 6
Sec: solve for "x" by isolating it > keep it on one side (left) > subtract 2x from both sides >
= 4x -2x + 3 > 2x - 2x - 6
= 2x + 3 > - 6
Third: subtract 3 from both sides >
= 2x + 3 - 3 > - 6 - 3
= 2x > - 9
Fourth: divide both sides by 2 >
= 2x/2 > - 9/2
= x > -9/2
2007-01-03 05:46:09 · answer #2 · answered by ♪♥Annie♥♪ 6 · 0⤊ 0⤋
x>-2/3
2007-01-02 20:33:37 · answer #3 · answered by frankie 1 · 0⤊ 1⤋
4x + 3 > 2x - 6
2x > -9
x > -9/2
for representing this in number line, put a round bracket '(' at -9/2 and darken the entire number line to the right of it.
Note that if the question were x ⥠-9/2, u hv to use '[' instead of '('
2007-01-02 20:27:41 · answer #4 · answered by ? 3 · 2⤊ 0⤋
4x + 3 > 2(x - 3)
4x + 3 > 2x - 6
2x > - 9
x > - 9/2
2007-01-02 20:31:25 · answer #5 · answered by Helmut 7 · 2⤊ 0⤋
4x + 3 > 2(x - 3)
4x + 3 > 2x - 6
4x + 3 - 2x > 2x - 6 - 2x
2x + 3 > - 6
2x + 3 - 3 > - 6 - 3
2x . - 9
2x/2 > - 9/2
x > - 9/2
x > - 4.5
The answer is x > - 4.5
- - - - -s-
2007-01-02 22:54:58 · answer #6 · answered by SAMUEL D 7 · 1⤊ 0⤋
4x+3>2(x-3)
4x+3>2x-6
4x-2x>-6-3
2x>-9
x>-4.5
Can't you draw this algebraic solution??!!!!!!!!!
>>Draw the number line i.e -ve side at your left hand side and +ve side at your right hand side, (centre is always zero)
>>At the top of -4 (should be at your left hand side), starting to draw an arrow towards your right hand side.
That is he solution of your answer
2007-01-02 20:33:02 · answer #7 · answered by Shark 1 · 0⤊ 0⤋
Expand the numbers on the right.
4x + 3 > 2x - 6
Then re-arrange them.
4x - 2x > -6 -3
2x > -9
The answer seems weird though... Maybe I'm wrong.
*shrug*
2007-01-02 20:28:18 · answer #8 · answered by Diamond 4 · 2⤊ 0⤋
Solve for x (replacing < with =) then plug the value of x into both sides of the original inequality equation to determine if the 'larger than' sign is true.
2007-01-02 23:27:05 · answer #9 · answered by Kes 7 · 0⤊ 1⤋
4x+3>2x-6
4x-2x>-6-3
2x>-9
x>-9/2
2007-01-03 00:54:40 · answer #10 · answered by mmmm n 2 · 1⤊ 0⤋