## need help on -2X - 4 < 10, (2/3)X + (1/6)X = 2

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
lchilds
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### need help on -2X - 4 < 10, (2/3)X + (1/6)X = 2

-2X - 4<10

(2/3)X + (1/6)X =2

stapel_eliz
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lchilds wrote:(2/3)X + (1/6)X =2

This is a linear equation. To solve, a good first step would be to multiply through by "6" to clear the denominators, and then combine the "like" terms on the left-hand side. Divide through by "5" to complete the solution.

lchilds wrote:-2X - 4<10

Solving linear inequalities is very similar to solving linear equations such as the previous exercise. In this case, a good first step would be to add "4" to both sides. The next obvious step would be to divide through by "-2"; this is where you encounter the one difference between equations and inequalities: when you multiply or divide through by a negative, you need to remember to reverse the inequality sign.

So after dividing through by "-2", you'll need to remember to switch the "less than" sign to a "greater than" sign. Then simplify the right-hand side to complete the solution.

If you get stuck, please reply showing how far you have gotten. Thank you!

lchilds
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Joined: Tue Mar 24, 2009 6:47 pm
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### Re: need help on -2X - 4 < 10, (2/3)X + (1/6)X = 2

when you say multiple through by 6 do you mean 6(2/3)x+6(1/6)x i am not really understanding this problem

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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lchilds wrote:when you say multiple through by 6 do you mean 6(2/3)x+6(1/6)x

To "multiply through" is to multiply on everything on either side of the equation or inequality. In this case:

. . . . .$6\left(\frac{2}{3}x\, +\, \frac{1}{6}x\right)\, =\, 6(2)$

. . . . .$6\left(\frac{2}{3}x\right)\, +\, 6\left(\frac{1}{6}x\right)\, =\, 12$

. . . . .$4x\, +\, 1x\, =\, 12$

...and so forth.

lchilds wrote:i am not really understanding this problem

A good way to gain some understanding might be to study the lesson on solving linear equations. By reading the explanations and doing all of the steps in the worked examples, you should be well on your way!