Answer: The equation is written as: " 7x + 28 = 8 − 3x " .
The value for x , when the equation is solved, is: " -2 ."
Explanation:
Let the "unknown number" be represented by the variable, x ;
7 (times) the [sum of: (x + 4)] ; (is the same as): 8 [decreased by]:
3(times)x ;
Rewrite: " 7(x + 4) = 8 − 3x ". This is the written expression.
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Now, if we wish to "solve for x" ;
Let's examine the 'left-hand side' of the equation:
7(x + 4) ;
Note the 'distributive property' of multiplication:
a(b + c) = ab + ac ;
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So: 7(x + 4) = 7*x + 7*4 = 7x + 28 ;
Now, let's write the entire equation:
7x + 28 = 8 − 3x ;
Let's add 3x , and subtract 8 ; from Each Side of the equation:
7x + 28 + 3x − 8 = 8 + 3x − 8 ;
→ 7x + 3x + 28 − 8 = 8 − 3x + 3x;
to get:
10x + 20 = 0 ;
Now: Subtract 20 from Each Side of the equation:
10x + 20 − 20 = 0 − 20 ;
to get:
10x = -20 ; Now, divide both sides of the equation by 10 ;
to isolate x on one side of the equation; & to solve for x :
10x/10 = -20/10 ;
to get: " x = - 2 " .
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Alternate method:
10x + 20 = 0 ;
Divide the Entire Equation by 10 ;
(10x + 20) / 10 = 0____ ;
to get: (10x/10) + (20/10) = 0 ;
→ x + 2 = 0 ;
Now subtract 2 from each side of the equation;
to isolate x on one side of the equation; & to solve for x :
x + 2 − 2 = 0 − 2 ;
to get: " x = -2 " .
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Answer:
The equation is written as:
" 7x + 28 = 8 − 3x " .
The value for x, when the equation is solved, is "-2".
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Hope this is helpful to you! Best wishes!
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