Answer: " 14 " .
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→ " x = 14 " .
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Explanation:
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First, let us simplify the expression on the "left-hand side" of the equation:
→ -2(1 −4x) ;
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Note the "distributive property of multiplication" :
→ a(b + c) = ab + ac .
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As such, we can rewrite:
→ -2(1 − 4x) = (-2)(1) + (-2)(-4x) ;
= - 2 + 8x ;
↔ 8x − 2 ;
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Now, rewrite the entire expression:
→ 8x − 2 = 3x + 8 ;
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Subtract "(3x)" from each side of the equation;
and add "2" to each side of the equation:
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→ 8x − 2 − 3x + 2 = 3x + 8 − 3x + 2 ;
to get:
→ 5x = 10 ;
Now, divide each side of the equation by "5" ;
to isolate "x" on side of the equation;
& to solve for "x" ;
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→ 5x/5 = 10/5 ;
to get:
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→ x = 2 .
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Now, let us check our work:
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Plug in "2" for all "x-values" into the original equation;
to see if the equation holds true;
that is, to see if each side of the original equation given has the same value;
when "x = 2" :
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Note the given equation:
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→ -2[1 − 4x] = 3x + 8 ;
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Start with the left-hand side:
→ -2[1 − (4*2)} = -2(1 − 8) = -2(-7) = 14 .
Now, continue with the right-hand side:
→ 3(2) + 8 = 6 + 8 = 14 .
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→ 14 =? 14 ??? ; Yes!
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Hope this is helpful to you!
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