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If (1)/(2)+4x=-x+2, what is the value of x ? Choose 1 answer: (A) x=(3)/(10) (B) x=(1)/(2) (c) x=(5)/(6) (D) x=(15)/(2)

If 12+4x=−x+2\frac{1}{2}+4x=-x+2, what is the value of xx?\newlineChoose 11 answer:\newline(A) x=310x=\frac{3}{10}\newline(B) x=12x=\frac{1}{2}\newline(C) x=56x=\frac{5}{6}\newline(D) x=152x=\frac{15}{2}

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Full solution

Q. If 12+4x=−x+2\frac{1}{2}+4x=-x+2, what is the value of xx?\newlineChoose 11 answer:\newline(A) x=310x=\frac{3}{10}\newline(B) x=12x=\frac{1}{2}\newline(C) x=56x=\frac{5}{6}\newline(D) x=152x=\frac{15}{2}
  1. Write down the equation: Write down the equation.\newline(12)+4x=−x+2(\frac{1}{2}) + 4x = -x + 2\newlineWe need to solve for xx.
  2. Combine like terms: Combine like terms by moving all xx terms to one side of the equation.\newlineTo do this, add xx to both sides of the equation to get all the xx terms on one side.\newline(12)+4x+x=−x+2+x(\frac{1}{2}) + 4x + x = -x + 2 + x\newlineThis simplifies to:\newline(12)+5x=2(\frac{1}{2}) + 5x = 2
  3. Isolate the x term: Isolate the x term by moving the constant term to the other side.\newlineTo do this, subtract (1/2)(1/2) from both sides of the equation.\newline(1/2)+5x−(1/2)=2−(1/2)(1/2) + 5x - (1/2) = 2 - (1/2)\newlineThis simplifies to:\newline5x=2−(1/2)5x = 2 - (1/2)
  4. Calculate the right side: Calculate the right side of the equation.\newline2−(12)2 - \left(\frac{1}{2}\right) is equal to (42)−(12)\left(\frac{4}{2}\right) - \left(\frac{1}{2}\right), which simplifies to 32\frac{3}{2}.\newlineSo the equation now is:\newline5x=325x = \frac{3}{2}
  5. Solve for x: Solve for x by dividing both sides of the equation by 55.\newlinex=(32)/5x = \left(\frac{3}{2}\right) / 5\newlinex=(32)⋅(15)x = \left(\frac{3}{2}\right) \cdot \left(\frac{1}{5}\right)\newlinex=310x = \frac{3}{10}

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