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)

Write Equation: Write down the equation. We have the equation 2 + 7z = -z - 4.Combine Z Terms: Add z to both sides to get all the z terms on one side. 2 + 7z + z = -z - 4 + z This simplifies to: 2 + 8z = -4Isolate Z Term: Subtract 2 from both sides to isolate the term with z. 2 + 8z - 2 = -4 - 2 This simplifies to: 8z = -6Solve for Z: Divide both sides by 8 to solve for z. 8z / 8 = -6 / 8 This simplifies to: z = -6 / 8Simplify Fraction: Simplify the fraction -6 / 8. -6 / 8 can be reduced by dividing both the numerator and the denominator by 2. z = (-6 / 2) / (8 / 2) z = -3 / 4

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Math Problems

Algebra 2

Evaluate variable expressions involving rational numbers

Full solution

Q. If

2+7z=-z-4

, what is the value of

z

\newline

Choose

1

answer:

\newline

(A)

z=-1

\newline

(B)

z=-\frac{3}{4}

\newline

(C)

z=-\frac{1}{3}

\newline

(D)

z=-\frac{1}{4}

Write Equation: Write down the equation. $\newline$ We have the equation $2 + 7z = -z - 4$ .
Combine Z Terms: Add $z$ to both sides to get all the $z$ terms on one side. $\newline$ $2 + 7z + z = -z - 4 + z$ $\newline$ This simplifies to: $\newline$ $2 + 8z = -4$
Isolate Z Term: Subtract $2$ from both sides to isolate the term with $z$ . $\newline$ $2 + 8z - 2 = -4 - 2$ $\newline$ This simplifies to: $\newline$ $8z = -6$
Solve for Z: Divide both sides by $8$ to solve for $z$ . $\newline$ $\frac{8z}{8} = \frac{-6}{8}$ $\newline$ This simplifies to: $\newline$ $z = \frac{-6}{8}$
Simplify Fraction: Simplify the fraction $-\frac{6}{8}$ . $-\frac{6}{8}$ can be reduced by dividing both the numerator and the denominator by $2$ . $z = \frac{-6 / 2}{8 / 2}$ $z = -\frac{3}{4}$