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iren2701 [21]
3 years ago
11

Please explain each step 5x-7=7x-17

Mathematics
1 answer:
EleoNora [17]3 years ago
6 0
Let's get the same terms on the same side.
I am going to remove 5x from both sides of the equation by subtracting 5x

5x - 5x<span> -7 = 7x -</span>5x<span> - 17</span>
           -7 = 2x - 17   now lets remove the 17 from both sides
       -7 + 17 = 2x     (why do we add 17?  Think of 2x -17 as 2x +  -17.  Tor remove a negative number we add it.
Now we finally have     10=2x and if we divide both sides by 2

<u>10</u><span>  = </span><u>2x</u><u>
</u>2       2    we get that x = 5
<u />Let's check by substituting 5 in the original equation:
5(5) - 7 = 7(5) - 17
25 - 7 = 35 - 17
<span>18      =       18</span>
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Five times the sum of a number and 27 is greater than or equal to six times the sum of that
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The complete version of question:

<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution of this problem.</em>

Answer:

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

Step-by-step explanation:

As the description of the statement is:

'<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26'.</em>

<em />

As

  • <em>Five times the sum of a number and 27  </em>is written as: 5(x + 27)
  • <em>greater than or equal </em>is written as:  \geq
  • <em>six times the sum of that number and 26'  </em>is written as: 6(x + 26)

so lets combine the whole statement:

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

solving

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

<em />5x+135\ge \:6x+156<em />

<em />5x+135-135\ge \:6x+156-135<em />

<em />5x\ge \:6x+21<em />

<em />5x-6x\ge \:6x+21-6x<em />

<em />-x\ge \:21<em />

<em />\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}<em />

<em />\left(-x\right)\left(-1\right)\le \:21\left(-1\right)<em />

<em />x\le \:-21<em />

Therefore,

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

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Step-by-step explanation:

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