5 times a number increased by 18 is the same as 36 more than times 4 times the number. Find the number

Step-by-step explanation:

Let's assume that that question is meant to read:

" 5 times a number increased by 18 is the same as 36 more than 4 times the number.  Find the number ".

Let the variable "x" (i.e. the lower-case letter ex]—represent the unknown number—for which we are asked to solve.

If the question/problem is meant to read:

 "  5 times a number increased by 18 is the same as 36 more than 4 times the number.  Find the number ".

Then, treat the problem as:

  " 5 times [a number increased by 18] " ; {is the same as}:  " 36 more than [4 times the number]".  Find the number ".

Note that:  " {is the same as:}" ;  means:  "equals:} ;

So:  "...[a number; that is, an unknown number; that is, "x" ;  increased by "18" ]" ;  would be represented by:  "[x + 18]" .

5 times that value would be represented as:

  →  5* (x + 18) ;   or:   "  5(x + 18) " .

Then we add the:  " = " ["equals"] sign:

Then, we consider:  "... 36 more than [4 times the number]" .

    4 times the [unknown number]:  would be written as:

         →  " 4 * x " ;   or simply:  " 4x " .

→  "36 more than this [the above value; i.e. "4x" ;  would be represented by adding "36" to said value; as follows:

          →  " 4x + 36 " ;

Now we can:

  1)  Write our expression as an equation;  and then:

  2)  Solve for the value for "x" ; our unknown number.

 Here is the expression, as an equation:

  →  5(x + 18) =  4x + 36 ;

Now, solve for "x" ;

Start with the "left-hand side" of the equation:

          →  5(x + 18) ;

Let us expand this expression.

Note the "distributive property" of multiplication:

   →  a(b+c) = ab + ac .

As such:  " 5(x + 18) = (5 * x)  +  (5 * 18) "  = 5x +120 .

Now, rewrite the equation:

  →  5x + 120 = 4x + 36 ;

Let us subtract "36" from each side of the equation; & subtract "4x" from each side of the equation:

                       →  5x + 120  =     4x  +  36 ;

                         - 4x   -  36  =   - 4x  -  36

         to get:        1x +  54  =      10 ;

Rewrite as:      " x + 54 = 10 "  ;

→  {Since:  "1x = x " ;  

        → {since:  (" 1 * [any numerical value] = that same numerical value"};

        Note that this refers to the "identity property of multiplication."

  →  

 → We have:   " x + 54 = 10 " ;  Solve for "x" ;

Subtract "54" from Each Side of the equation;

 to isolate "x" on one side of the equation; & to solve for "x" ;

       →  " x + 54 - 54 = 10 - 54 " ;

 to get:  " x = -44 " .

 The number is " - 44 " .

Let us substitute this value into our equation;  to check our work:

→  5(x + 18) =  4x + 36 ;

→  5(-44 + 18) ≟ 4(-44) + 35 ??  ;

→  5(-26) ≟ -176 + 35 ?? ;

→  -130   ≟ -176 + 35

step-by-step explanation: