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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Cumulative Assessment

Exercise 5 Page 99

Solve the equation for x. Then check for which values of a it is positive.

-2, -1, 0, and 1

Practice makes perfect

Let's start by solving the given equation for x.

3(2x-4)=4(ax-2)

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Solve for x

Distribute 3

6x-12=4(ax-2)

Distribute 4

6x-12=4ax-8

LHS+12=RHS+12

6x=4ax+4

LHS-4ax=RHS-4ax

6x-4ax=4

Factor out x

x(6-4a)=4

.LHS /4.=.RHS /4.

x=4/6-4a

We can see that the numerator is a positive number. Because the fraction needs to simplify to a positive number, we need the denominator to be positive as well. 6-4a>0 Let's solve this inequality for a.

6-4a>0

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Solve for a

LHS-6>RHS-6

-4a>-6

Flip inequality and change signs

4a<6

.LHS /4.<.RHS /4.

a<6/4

a/b=.a /2./.b /2.

a<3/2

Write as a decimal

a<1.5

When a<1.5 the solution of the equation is positive. We can identify those from the given values. -2, -1, 0, 1

Subchapter links

Exercises p.98-99