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WyzAnt Tutoring Tutor Tutor United States

German and English Language Teacher

Montclair, NJ (07042)

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13x-18=-5x+36

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Asked by Keysha from Wilson, NC
10

Keysha, are you looking for a solution / answer? Right now it's just an equation, so nothing to justify yet...?

You need to move the x's to one side and the numbers to the other. There are always several ways to do this.

Here's one:
13x - 18 = -5x + 36    [now add 18 on both sides]

13x        = -5x + 54    [now add 5x on both sides]

18x       = 54              [now divide by 18]

x        = 3

-3+x<-2+1 how to solve

how to solve -3+x<-2+1

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Asked by Theresa from Augusta, GA
10

Hi Theresa,

you already have the solution from John, just an additional piece of advice: always separate the x on one side and the numbers on the other side of these problems. Here: -3 + x < .... means you could for example add +3 on both sides. On the left side is now just x. On the right you have -2 + 1 +3 (which equals 2 as John showed in his solution).

CAUTION: the problems with < or > (as opposed to = ) have a specialty: when you multiply with a negative number (say you multiply both sides by -2) then your arrow changes directions!

Why does the inequality sign change when both sides are multiplied or divided by a negative number?

Does this happen with equations? Explain why or why not?
Give all the symbols that make 5 + 8 ___ 13 true? Explain.

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Asked by Jamal from Oregon, OH
00

Hi Jamal,

this does NOT happen with equations. Only inequalities. The inequality would not be true anymore after dividing / multiplying with a negative number. You can use an example to show this. Let's say:
-12x > 12 is your inequality to be solved. Just like in an equation your next step is to divide both sides by (-12). You will get to x < -1. Think about it: The only way that -12*x can ever be bigger than +12, is when x is negative and its value more than one. Which is expressed by x < -1. Try it out. Use -1.2, -2, -3 and see whether the result is bigger than 12. Then try -1, -0.8, 0 and +1 and see if that would still be true? No? so, your x needs to be smaller than -1.

What is the solution using the quadratic formula to solve x^2-3x+9/4=0

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Asked by Ty from Lexington, SC
00

Hello Ty,

you will need both the binomial formula here and the "complete the square" step to transform your equation. The expression on the left happens to be a perfect binomial already and you can transform it to its basic expression being (x-3/2)^2.
Now the only way that this expression is ever zero, is when the value in brackets is zero. Which is only true when x=3/2. Then you'll have (3/2 - 3/2)^2 = 0 or 0^2=0

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