Algebra 2 equation with fractions

Question

Solve 1/2 - (4/9)x = 6/5 - (11/8)x

Put x in simplified form

Answer 1

Solve 1/2 - (4/9)x = 6/5 - (11/8)x

As your tutor, I'll teach you both some facts that you need to have memorized, and some guiding rules of thumb or guiding intuitions that you can use to understand this problem and to solve other problems, even entirely new ones.

If you're in Algebra 2, you've probably solved many equations before. But you may have relied on memorizing procedures.

Remember, our goal is to get x by itself on one side of the equals sign. Here are some guiding rules of thumb you can use for really understanding how to solve equations.

1. x may appear in multiple terms
2. You are getting closer when all of the x terms are on the same side of the equals sign.
3. You can combine terms with x.
4. You are getting closer when all x terms are combined.

If you follow these guiding rules, you'll get the equation now to a single-step equation, and you'll be confident at that point.

One reason this equation is not solved is that there are x's on both sides of the equals sign. Let's fix that. Let's move the -(11/8)x term to the other side. As you are in Algebra 2 now, I'm going to assume you know that we can add (11/8)x to each side of the equation. (If you don't, we can drill that.)

1/2 - (4/9)x + (11/8)x = 6/5

Now all the x terms are on one side. Notice how that looks closer to being solved.

But there is a non-x term (1/2) term on that side. Let's fix that. Subtract 1/2 from both sides.

(4/9)x + (11/8)x = 6/5 - 1/2

Not only are the x terms on one side now, but there are no other terms on that side.

Let's get this closer to being solved by combining x terms.

( -4/9 + 11/8) x = 6/5 - 1/2

I'm going to assume you know how to add and subtract fractions:

(65/72)x = 7/10

This is much closer to being solved! At this point you should recognize it as a 1-step equation. Multiply both sides by 72/67.

(72/67)(67/72)x = (72/67)(7/10)

x = 252/335

Answer 2

1/2 - (4/9)x = 6/5 - (11/8)x

Add (11/8)x to both sides and subtract 1/2 from both sides:

(67/72)x = 7/10

Note: (11/8) - (4/9) = (99/72) - (32/72) = 67/72.

and (6/5) - (1/2) = (12/10) - (5/10) = 7/10

(Combining using common denominators.)

67*10x = 72*7

670x = 504

x = 504/670

x = 252 / 335

Note: 2 is the only common factor of the numerator and denominator. Factorization into primes shows this.

Itis important at this point to check the answer. That's very easy, using a scientific calculator.