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# if 5x - 17 = -x + 7, then x =

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if 5x - 17 = -x + 7, then x =

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Jun 1, 2019

#1
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5x - 17 = -x + 7

5x - 17 + 17 = -x + 7 + 17

5x = -x + 24

5x + x = -x + 24 + x

6x = 24

Divide 6 on both sides

$$\frac{6x}{6} = \frac{24}{6}$$

x = 4

x equals 4

Hope this helps ;P

Jun 1, 2019
edited by EmeraldWonder  Jun 1, 2019
#2
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I just like to add it a diffrent way even though but Emerald wonder is spot on correct.

$$5x - 17 = -x + 7$$

first we gather LIKE TERMS, and when looking at the problem we see that we have 5x and -x on the other side of the equation so now you must gather those two x varibles to the rigth side of the equation so we can solve for x, and even though the x were carrying over is negative it becomes positive because when we carry numbers to another side of an equation we change them to there inverse or recipical wether its a fraction or not.

$$6x - 17 = 7$$

now what we have to do is to make 6x = to the value on the other side of the equation and we can do this by carrying -17 over (In Algebra we pair the sign that is to the left of a number a rule I like to think of it as is that there is no subtraction in algebra only adding of sign's so a good rule to use is that and can be applied to regular mathmatic's as welll not just algebra. after we carry the negative 17 over it becomes a positive 17 and adding that to 7 is 24

$$6x = 24$$

Now are current problems state's 6 time's x is equal to 24 all we have to do is divide 24 by the coefficient of x which is 6 and 24 divided by 6 give's us the quotinet of 4 so this must mean

$$x = 4$$

we can check this by pluging this back into the original equation

$$5(4) - 17 = -(4) + 7$$   so lets check this   5*4  - 17 = 3 and -4 + 7 = 3

THE SOLUTION IS CORRECT! x is equal to 4