Mathematics, 22.08.2019 16:30, carlomorales200

Consider solving the equation for x.
3(3x + 4) - 5 = ax + b
which statements are true about the solution to the equation when substituting values for a and b as specified?
select all that apply.
a. if a=−3 and b=4 , then there is exactly one solution to the equation.
b. if a=−9 and b=13 , then there is no solution to the equation.
c. if a=9 and b=−2 , then there is no solution to the equation.
d. if a=−3 and b=−5 , then there are infinitely many solutions to the equation.
e. if a=9 and b=7 , then there is exactly one solution to the equation.

Answers: 1

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Answers

A. If a=−3 and b=4 , then there is exactly one solution to the equation.C. If a=9 and b=−2 , then there is no solution to the equation.

Step-by-step explanation:

The given equation is

3(3x+4)-5=ax+b

To solve for , we need to use the distributive property

$3(3x+4)-5=ax+b\\9x+12-5=ax+b\\9x-ax=b-7\\x(9-a)=b-7$

To find the right statement, we need to the given values.

For a=-3 and b=4,

$x(9-a)=b-7\\x(9-(-3))=4-7\\x(9+3)=-3\\12x=-3\\x=\frac{-3}{12} =-\frac{1}{4}$

So, choice A is true, because there's one solution to the equation.

For a=-9 and b=13,

$x(9-a)=b-7\\x(9-(-9))=13-7\\18x=6\\x=\frac{6}{18}=\frac{1}{3}$

The choice B is false.

For a=9 and b=-2

$x(9-a)=b-7\\x(9-9)=-2-7\\0x=-9\\0=-9$

Choice C is correct, because there's no solution, because zero is not equal to -9.

For a=-3 and b=-5

$x(9-a)=b-7\\x(9-(-3))=-5-7\\12x=-12\\x=\frac{-12}{12}=-1$

Choice D is false, becuase there's only one solution.

For a=9 and b=7

$x(9-a)=b-7\\x(9-9)=7-7\\0x=0\\0=0$

Choice E is false, because there are infinite solutions in ths case.

Therefore, the right choices are A and C.

answered: Guest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

answered: Guest

answer: the answer is b. i think hope i got it correct

step-by-step explanation:

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Consider solving the equation for x.
3(3x + 4) - 5 = ax + b
which statements are true ab...