SOLUTION: Would I add 4 to both sides to solve this? The first step would be 5 *2 = 6 and so on, right? How to solve?
5(2x+3)≥4(6x-1)
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-> SOLUTION: Would I add 4 to both sides to solve this? The first step would be 5 *2 = 6 and so on, right? How to solve?
5(2x+3)≥4(6x-1)
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You can put this solution on YOUR website! How to solve?
5(2x+3)≥4(6x-1)
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10x+15 >= 24x-4
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Subtract 10x from both sides.
Add 4 to both sides.
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19 >= 12x
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Divide both sides by 12.
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19/12 >= x
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Write from left to right:
x <= 19/12
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Cheers,
Stan H.
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You can put this solution on YOUR website! You can work these just as you would work an equation with the exception that any time you multiply or divide both sides of the inequality by a minus number, you reverse the direction of the inequality sign.
So we start with:
5(2x + 3) >= 4(6x - 1)
On the left side multiply 5 times both quantities in the parentheses to make the inequality become:
10x + 15 >= 4(6x - 1)
Next on the right side multiply 4 times both quantities in the parentheses to make the inequality become:
10x + 15 >= 24x - 4
Gather the x terms on the left side by subtracting 24x from both sides to get:
10x - 24x + 15 >= - 4
Then subtract 15 from both sides to gather all the plain old numbers on the right side and you have:
10x - 24x >= - 4 - 15
On the left side combine the two x terms by subtracting 24x from 10x to get:
-14x >= - 4 - 15
On the right side add the two negative numbers to get:
-14x >= - 19
Next to solve for x we divide both sides by the coefficient of x ... that is we divide by -14 and get:
(-14/-14)x >= -19/-14
and the inequality becomes:
x >= 19/14
But don't forget the rule ... if you divide or multiply both sides of the inequality by a negative quantity, you must reverse the inequality sign. We divided both sides by -14 and therefore we must reverse the inequality sign to get the answer of:
x <= 19/14
In his answer Stanbon went through basically the same process. However, he subtracted 10x from 24x and got the minor error of 12x instead of 14x. The correct answer is x <= 19/14 instead of x <= 19/12.
Hope this helps you understand how to work inequalities a little better. For inequalities you can use most of the rules that you already know for solving equations. Just don't forget the rule about reversing the inequality sign any time you multiply or divide by a negative number.
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