Answers:
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1) " x = -6 " .
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2) " x = 8 " .
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3) " x = 3 " .
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Step-by-step explanation:
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1) " -7x = 42 " ; Solve for "x" ;
Divide each side by "-7" ;
-7x / -7 = 42/ -7 ;
x = - 6 .
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2) " 2(x − 4) − 15 = - 7 " ; Solve for "x" ;
Add "15" to each side of the equation ;
" 2(x − 4) − 15 + 15 = - 7 + 15 ;
→ " 2(x − 4) = 8 " ;
Now, divide each side of the equation by "2" ;
→ [ 2(x − 4) ] / 2 = 8 / 2 ;
to get: "(x − 4) = 4 " ;
Add "4" to each side of the equation;
to isolate "x" on one side of the equation; and to solve for "x" ;
→ x − 4 + 4 = 4 + 4 ;
to get: " x = 8 " .
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3) "6x − 2 = 4(x + 1 ) "
→ Factor out a "2" from "6x − 2" :
→ " 2(3x − 1) " ;
Rewrite the equation as:
→ " 2(3x − 1) = 4(x + 1) '" ;
Now, divide EACH SIDE of the equation by "2" ;
→ " [ 2(3x − 1) ] / 2 = [ 4(x + 1) ] / 2 " ;
to get:
→ 3x − 1 = 2(x + 1) .
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Now, let us simplify the "right-hand side" of the equation ;
Note the "distributive property of multiplication" :
a (b + c) = ab + ac ;
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As such: " 2(x + 1) = (2*x) + (2*1`) = 2x + 2 ;
Now, rewrite the equation:
→ " 3x − 1 = 2x + 2 " ;
Subtract "2x" from each side of the equation; & Add "1" to each side of the equation:
→ " 3x − 1 − 2x + 1 = 2x + 2 − 2x + 1 ;
to get:
x = 3 .
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