If q(x) = 5-7x, find x if q(-2x) = 12.

[Sparkwi44]

I'm having trouble figuring out where to begin. The year just started, so my knowledge is foggy and algebra 2 is throwing me for a loop. The paths I'm trying to take to solve this don't work. Solving for x on either function of q gives me a weird fraction, substitution doesn't work either, and I tried to just make x equal -6, since -2*-6=12... but 5-7(-6) gives me -37, which doesn't feel right either.

I don't know if I'm overthinking it or underthinking it, and I would kindly appreciate your help.

 

[BigBeachBanana]

I'm having trouble figuring out where to begin. The year just started, so my knowledge is foggy and algebra 2 is throwing me for a loop. The paths I'm trying to take to solve this don't work. Solving for x on either function of q gives me a weird fraction, substitution doesn't work either, and I tried to just make x equal -6, since -2*-6=12... but 5-7(-6) gives me -37, which doesn't feel right either.

I don't know if I'm overthinking it or underthinking it, and I would kindly appreciate your help.

[math]q(x) =5-7x \implies q(-2x) = 5-7(-2x) = 12[/math]

 

[stapel]

I'm having trouble figuring out where to begin. The year just started, so my knowledge is foggy and algebra 2 is throwing me for a loop. The paths I'm trying to take to solve this don't work. Solving for x on either function of q gives me a weird fraction, substitution doesn't work either, and I tried to just make x equal -6, since -2*-6=12... but 5-7(-6) gives me -37, which doesn't feel right either.

Please reply *showing* your work that led to the mentioned results. Thank you!

 

[Steven G]

1st: Determine what you take q of to get 12.
2nd: Set -2x equal to the answer from step1.
3rd: Solve step 2 for x.
4th: Smile because you are done.

 

[The Highlander]

I tried to just make x equal -6, since -2*-6=12... but 5-7(-6) gives me -37, which doesn't feel right either.

In Post #2, @BigBeachBanana has succinctly illustrated how to solve for x as efficiently as possible but what concerns me is how you arrive at: "5-7(-6) gives me -37"!

You seem to understand that, for multiplication & division, like signs give positive results (ˉ2 × ˉ6 = 12) but you don't appear to know that subtracting a negative is equivalent to adding the positive. (5 - 7 × ˉ6 actually "gives" 47!)

You may need to revise your handling of negative numbers in Arithmetic operations (or just be a bit more careful, if you're sure you do know all the 'rules'. ?)

Please come back and tell us what value you now get for x. Thank you. ?

 

[Steven G]

I tried to just make x equal -6, since -2*-6=12... but 5-7(-6) gives me -37, which doesn't feel right either.

There is no reason at all to expect q(12) to equal 12. Please thing about that. You want q(something) to equal 12. Find the something and then set it equal to -2x. Then solve for x.

 

[Steven G]

I like these type problems and will show a solution here.

If q(x) = 5-7x, find X if q(-2X) = 12

Solve 5-7x=12. We know that 5 + 7 =12, so it is true that 5 - (-7) = 12. Then 7x = -7 or x=-1. That is, q(-1) = 12 = q(-2X)

Since q (ONLY -1) = 12, it must be true that -2X = -1. Finally X=1/2

 

[The Highlander]

Or (perhaps more simply), as @BigBeachBanana said:-

[math]q(x) =5-7x \implies \color{red}q(-2x) = 5-7(-2x) = 12[/math]

          and​

[math]5-7(-2x) = 12 \\ \implies 5+14x=12         \\ \implies 14x=12-5         \\ \implies 14x=7             \\ \implies x=\frac{7}{14}              \\ \implies x=\frac{1}{2}               [/math]
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