# Solving a 2 step equation Involving Rational Numbers

by Monica Marie
(Virginia)

2/3 = -1 5/9 + 5/8x

I'm getting stuck on finding the common denominator with a mixed number to get this answer. Help!!

Karin from Algebra Class Says:

The first thing that you must do is convert the mixed number to an improper fraction.

-1 5/9 = -14/9 as an improper fraction.

Then you can begin solving by getting rid of the fraction. The least common multiple for 3, 9, and 8 is 72. Therefore, you must multiply all terms by 72.

722/3 = 72-14/9 + 5/8x

48 = -112 + 45x

Now that you don't have any fractions, it's much easier to solve this 2 step problem.

Step 1: Add 112 to both sides.

48 + 112 = -112 + 112 + 45x

160 = 45x

Step 2: Divide by 45 on both sides

160/45 = 45x/45

32/9 = x

2/3 = -14/9 + 5/8(32/9)
2/3 = 2/3

I hope this helps,
Karin

### Comments for Solving a 2 step equation Involving Rational Numbers

Average Rating     Nov 07, 2013 Rating     help NEW by: Anonymous 3/B + P/4 = 3/4

 Jan 28, 2013 Rating     HELP ME!!! by: Anonymous i need help on this problem 1 and 3 5ths-1 3rd y = -1 and 8 9ths

 Sep 12, 2012 Rating     rational numbers and equations by: Anonymous i need help on 32x17/24

 Aug 30, 2012 Rating     Two step equations by: Anonymous I need help on this problem z + 9 divided 4 = 2.1

 Jun 28, 2012 Rating     help by: Anonymous i need help on this now. 1.3-5r=7.4

 May 16, 2012 Rating     help on homework by: sierra i need help on this equation 2/3 x + 3/9 = 5/9 find x?

 Jan 15, 2012 Rating     helpful by: rakayla this website was very helpful i am doing a little better in math and my teacher sees progress and a change in me and so will my parents

 Nov 21, 2011 Rating     Two Step Equation by: Anonymous What is 1/3x-5=30____________________________________________________Karin from Algebra class Says:For the equation, 1/3x - 5 = 30, I would start by adding five to both sides:1/3x - 5+5 = 30+51/3x = 35Now you can isolate x by multiplying both sides by 3.3(1/3x) = 35(3)x = 105Hope this helps,Karin

 Oct 04, 2011 Rating     Two Step Equation by: Anonymous 5/9+x=2/3____________________________________________________Karin from Algebra Class Says:5/9 + x = 2/3In this problem, we have two fractions. We need to multiply all terms by the least common multiple (of the denominators), and this will get rid of the fractions.The least common multiple of 9 and 3 is 9. Therefore, we will multiply all terms by 9.9[5/9 + x] = 2/3(9)5+ 9x = 6Now solve the two step equation.Subtract 5 from both sides.5-5 +9x = 6-59x = 1Divide by 9 on both sides9x/9 = 1/9x = 1/9.Check your answer by substituting.5/9 + 1/9 = 6/96/9 can be simplified to 2/3. Therefore, my answer is correct.x = 1/9.Hope this helps!!!

 Sep 09, 2011 Rating     I'm stuck!!!! by: Anonymous Do u know what is 3x/4-1/2=4what does x=?____________________________________________________Karin from Algebra Class Says: SFor the problem:3x/4 - 1/2 = 4First get rid of the fraction by multiplying by 4.4[3x/4-1/2] = 4(4) Notice that I multiply all terms by 4 on both sides!3x - 2 = 16Now solve as a two step equation by first adding 2 to both sides.3x-2+2 = 16+23x = 18Now divide by 3 on both sides.3x/3 = 18/3x = 6Check by substituting 6 into the original equation:(3*6/4) - 1/2 = 44=4The final answer is x = 6.The key is getting rid of the fraction first!!Hope this helps,Karin

 Sep 01, 2011 Rating     Solving Equations with Rational Numbers by: Anonymous 1.5d=3/8____________________________________________________Karin from Algebra Class Says:For the problem:1.5d = 3/8This problem seems more confusing because you have decimals and fractions. Decimals are a little easier to work with than fractions, so I would start by multiplying all terms by 8 to get rid of the fraction.8(1.5d) = 3/8(8)12d = 3 Now you don't have decimals or fractions!To solve, subtract 12 from both sides:12d/12 = 3/12d = 1/4 (3/12 simplified is 1/4)Check by substituting:1.5(.25) = .375 which is 3/8.375 = .375The final answer is d = 1/4 or d = .25Hope this helps,Karin

 Jun 09, 2011 Rating     Math iz hard by: Anonymous good very good Need More Help With Your Algebra Studies?