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yulyashka [42]
3 years ago
13

I need help solving this problem

Mathematics
1 answer:
zloy xaker [14]3 years ago
4 0

9514 1404 393

Explanation:

When something is subtracted from both sides of the equation, the justification is the <em>subtraction property of equality</em>. When something multiplies both sides of the equation, the justification is the <em>multiplication property of equality</em>. (This should not be a mystery.)

Here, the equation is solved by subtracting 17/3, then subtracting 1/2x, then multiplying by the inverse of the coefficient of x. After each of these steps is a simplification.

  \begin{array}{cc}\dfrac{17}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5&\text{given}\\\\\dfrac{17}{3}-\dfrac{3}{4}x-\dfrac{17}{3}=\dfrac{1}{2}x+5-\dfrac{17}{3}&\text{subtraction property ...}\\\\-\dfrac{3}{4}x=\dfrac{1}{2}x-\dfrac{2}{3}&\text{simplify}\\\\-\dfrac{3}{4}x-\dfrac{1}{2}x=\dfrac{1}{2}x-\dfrac{2}{3}-\dfrac{1}{2}x&\text{subtraction property ...} \end{array}

  \begin{array}{cc}-\dfrac{5}{4}x=-\dfrac{2}{3}&\text{simplify}\\\\-\dfrac{5}{4}x\times-\dfrac{4}{5}=-\dfrac{2}{3}\times-\dfrac{4}{5}&\text{multiplication property ...}\\\\x=\dfrac{8}{15}&\text{simplify} \end{array}

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