How many solutions does this equation have? –4 + 4z = 5z Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable z: Isolate the variable z on one side of the equation. –4 + 4z = 5z Subtract 4z from both sides to get: –4 = 5z - 4zSimplify equation: Simplify the right side of the equation by combining like terms. –4 = 5z - 4z –4 = zCheck solution validity: Check if the solution is valid. Substitute z with –4 into the original equation to verify: –4 + 4(-4) = 5(-4) –4 - 16 = -20 –20 = –20 This shows that the solution z = –4 satisfies the original equation.Determine number of solutions: Determine the number of solutions. Since we found a specific value for z that satisfies the equation, there is only one solution.

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How many solutions does this equation have? $\newline$ $-4 + 4z = 5z$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions $\newline$

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does this equation have?

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-4 + 4z = 5z

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Choices:

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(A)no solution

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(B)one solution

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(C)infinitely many solutions

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Isolate variable $z$ : Isolate the variable $z$ on one side of the equation. $\,-4 + 4z = 5z$ Subtract $4z$ from both sides to get: $\,-4 = 5z - 4z$
Simplify equation: Simplify the right side of the equation by combining like terms. $\newline$ $-4 = 5z - 4z$ $\newline$ $-4 = z$
Check solution validity: Check if the solution is valid. $\newline$ Substitute $z$ with $–4$ into the original equation to verify: $\newline$ $–4 + 4(–4) = 5(–4)$ $\newline$ $–4 - 16 = -20$ $\newline$ $–20 = –20$ $\newline$ This shows that the solution $z = –4$ satisfies the original equation.
Determine number of solutions: Determine the number of solutions. Since we found a specific value for $z$ that satisfies the equation, there is only $1$ solution.