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: Simplify the equation by combining like terms on each side. 60z + 50 - 97z = -37z + 49 Combine the z terms on the left side: 60z - 97z = -37z This simplifies to: -37z + 50 = -37z + 49Isolate Constant Terms: Now, subtract -37z from both sides to isolate the constant terms. -37z + 50 - (-37z) = -37z + 49 - (-37z) This simplifies to: 50 = 49Identify Contradiction: We see that 50 does not equal 49, which is a contradiction. This means there are no values of z that will satisfy the equation. Therefore, the equation has no solutions.

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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: Simplify the equation by combining like terms on each side. $\newline$ $60z + 50 - 97z = -37z + 49$ $\newline$ Combine the $z$ terms on the left side: $60z - 97z = -37z$ $\newline$ This simplifies to: $-37z + 50 = -37z + 49$
Isolate Constant Terms: Now, subtract $-37z$ from both sides to isolate the constant terms. $\newline$ $-37z + 50 - (-37z) = -37z + 49 - (-37z)$ $\newline$ This simplifies to: $50 = 49$
Identify Contradiction: We see that $50$ does not equal $49$ , which is a contradiction. This means there are no values of $z$ that will satisfy the equation. Therefore, the equation has no solutions.