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If 2+7z=-z-4, what is the value of z ? Choose 1 answer: (A) z=-1 (B) z=-(3)/(4) (c) z=-(1)/(3) (D) z=-(1)/(4)

If 2+7z=−z−42+7z=-z-4, what is the value of zz?\newlineChoose 11 answer:\newline(A) z=−1z=-1\newline(B) z=−34z=-\frac{3}{4}\newline(C) z=−13z=-\frac{1}{3}\newline(D) z=−14z=-\frac{1}{4}

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Full solution

Q. If 2+7z=−z−42+7z=-z-4, what is the value of zz?\newlineChoose 11 answer:\newline(A) z=−1z=-1\newline(B) z=−34z=-\frac{3}{4}\newline(C) z=−13z=-\frac{1}{3}\newline(D) z=−14z=-\frac{1}{4}
  1. Combine like terms: Write down the given equation and combine like terms.\newlineWe have the equation 2+7z=−z−42 + 7z = -z - 4.\newlineTo combine like terms, we need to get all the zz terms on one side and the constant terms on the other side.
  2. Move z terms to one side: Add zz to both sides of the equation to move the zz terms to one side.\newline2+7z+z=−z−4+z2 + 7z + z = -z - 4 + z\newlineThis simplifies to:\newline2+8z=−42 + 8z = -4
  3. Move constant terms to other side: Subtract 22 from both sides of the equation to move the constant terms to the other side.\newline2+8z−2=−4−22 + 8z - 2 = -4 - 2\newlineThis simplifies to:\newline8z=−68z = -6
  4. Solve for z: Divide both sides of the equation by 88 to solve for z.\newline8z8=−68\frac{8z}{8} = \frac{-6}{8}\newlineThis simplifies to:\newlinez=−68z = \frac{-6}{8}
  5. Simplify the fraction: Simplify the fraction −68-\frac{6}{8} to its lowest terms.\newline−68-\frac{6}{8} can be simplified by dividing both the numerator and the denominator by 22.\newlinez=−6/28/2z = \frac{-6 / 2}{8 / 2}\newlinez=−34z = -\frac{3}{4}

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