Answer:
Step-by-step explanation:
Let's assume that that question is meant to read:
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" 5 times a number increased by 18 is the same as 36 more than 4 times the number. Find the number ".
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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:
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" 5 times a number increased by 18 is the same as 36 more than 4 times the number. Find the number ".
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Then, treat the problem as:
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" 5 times [a number increased by 18] " ; {is the same as}: " 36 more than [4 times the number]". Find the number ".
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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:
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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 " ;
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Now we can:
1) Write our expression as an equation; and then:
2) Solve for the value for "x" ; our unknown number.
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Here is the expression, as an equation:
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→ 5(x + 18) = 4x + 36 ;
Now, solve for "x" ;
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Start with the "left-hand side" of the equation:
→ 5(x + 18) ;
Let us expand this expression.
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Note the "distributive property" of multiplication:
→ a(b+c) = ab + ac .
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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
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to get: 1x + 54 = 10 ;
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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."
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→
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→ 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 " .
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Answer: The number is " - 44 " .
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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
