Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
5. Rewriting Equations and Formulas
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Exercise 26 Page 40

Take a closer look at the first step. Are the expressions on the right-hand side equivalent?

x=10+3b/a

Practice makes perfect

Let's take a look at the first step in the given solution.

In the attempted solution an x was factored out — this is the error. The variable could not have been factored out from both terms, since the second term does not involve x. Let's distribute x in the second expression to see that the expressions on the right-hand side are not equivalent.
x(a-3b)
x* a - x * 3b
ax-3xb
We see that what we got is not the same as what we started with in the first line. ax-3xb ≠ ax -3b Instead, we should solve for x by first adding 3b to both sides of the equation.
10=ax-3b
10+3b=ax
10+3b/a=x
x=10+3b/a