How many solutions does the following equation have? -9(z+8)=-9z-72 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Simplify the left side: Simplify the left side of the equation by distributing -9 into the parentheses. -9(z+8) = -9z - 9*8 = -9z - 72Compare both sides: Now we have the equation -9z - 72 = -9z - 72. Compare both sides of the equation. Since the left side is identical to the right side, the equation is true for all values of z.Determine number of solutions: Determine the number of solutions. Since the equation is true for all values of z, the equation has infinitely many solutions.

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How many solutions does the following equation have?

-9(z+8)=-9z-72
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-9(z+8)=-9z-72$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

-9(z+8)=-9z-72

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Simplify the left side: Simplify the left side of the equation by distributing $-9$ into the parentheses. $\newline$ $-9(z+8)$ $\newline$ $= -9z - 9 \times 8$ $\newline$ $= -9z - 72$
Compare both sides: Now we have the equation $-9z - 72 = -9z - 72$ . $\newline$ Compare both sides of the equation. $\newline$ Since the left side is identical to the right side, the equation is true for all values of $z$ .
Determine number of solutions: Determine the number of solutions. $\newline$ Since the equation is true for all values of $z$ , the equation has infinitely many solutions.