How to Solve [(1/4)x+3] < or = to [(1/3)x+2] for X, (Algebra for Student Nurses)

This Article will give detailed instructions on how to solve this particular inequality that contains fractions. All similar inequalitys of this form can be solved using the same type of instructions.

Things You'll Need

• Paper
• and Pencil

Instructions

1. 

   This inequality contains fractions, with denominators 4 and 3. We need to clear the inequality of fractions, by finding the Least Common Denominator (LCD), and multiplying each term by this LCD. In order to find the LCD, we multiply the denominators together. This will give us (4)x(3)=12. The LCD is 12. Please click on the image for a better understanding.

2. 

   Now, we need to multiply each term in the inequality by the LCD, 12. This will give the following equivalent inequality: 12[(1/4)x]+12[3]< or =12[(1/3)x]+12[2]. We now divide 60 by the denominators of the fractions. This will give us the inequality: 3x+36< or =4x+24. The fractions are now gone. PLease click on the image for a better understanding.

3. 

   Now, we need to subtract 4x from both sides of the inequality, so that all x's are on the left hand side. This will give us 3x-4x+36 < or = 4x-4x+24, which is equal to -x+36< or =24. Similarly, we subtract 36 from both sides of the inequality, so that the constants are on the right hand side. This will give us -x+36-36< or =24-36, which is equal to -x< or = -12. Please click on the image for a better understanding.

4. 

   We now need to divide both sides by the coefficient of x, (-1). When we divide an inequality by a negative number, we have to switch the inequality sign, from < to >. This will give us the final answer, which is x> or = 12. Please click on the image for a better understanding.

5. 

   We now need to graph this solution. To do this, draw a number line, and draw a filled in circle at x=12, with an arrow pointing towards positive infinity. We then need to write it in Interval Notation. This is: [12, + infinity). Please Click on the Image for a better Understanding.

Tips & Warnings

• There are many methods that can be used to solve this inequality. The procedure used in this article is the one that is most convenient and efficient.