How many solutions does the following equation have? 60 z+50-97 z=-37 z+49 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Combine like terms: Combine like terms on both sides of the equation. 60z + 50 - 97z = -37z + 49 Combine the z terms on the left side: (60z - 97z) + 50 = -37z + 49 This simplifies to: -37z + 50 = -37z + 49Isolate the variable z: Attempt to isolate the variable z on one side. However, we notice that the z terms on both sides of the equation are the same, -37z. This means that if we subtract -37z from both sides, the z terms will cancel out. -37z + 50 - (-37z) = -37z + 49 - (-37z) This simplifies to: 50 = 49Analyze the resulting statement: Analyze the resulting statement. The statement 50 = 49 is false. This means that there is no value of z that will satisfy the equation, as the non-variable terms do not equal each other.

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How many solutions does the following equation have?

60 z+50-97 z=-37 z+49
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $60z + 50 - 97z = -37z + 49$ $\newline$ 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

60z + 50 - 97z = -37z + 49

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Combine like terms: Combine like terms on both sides of the equation. $\newline$ $60z + 50 - 97z = -37z + 49$ $\newline$ Combine the $z$ terms on the left side: $(60z - 97z) + 50 = -37z + 49$ $\newline$ This simplifies to: $-37z + 50 = -37z + 49$
Isolate the variable $z$ : Attempt to isolate the variable $z$ on one side. $\newline$ However, we notice that the $z$ terms on both sides of the equation are the same, $-37$ z. This means that if we subtract $-37$ z from both sides, the $z$ terms will cancel out. $\newline$ $-37$ z + $50$ - ( $-37$ z) = $-37$ z + $49$ - ( $-37$ z) $\newline$ This simplifies to: $50$ = $49$
Analyze the resulting statement: Analyze the resulting statement. $\newline$ The statement $50 = 49$ is false. This means that there is no value of $z$ that will satisfy the equation, as the non-variable terms do not equal each other.