How many solutions does this equation have? 3z = 5z + 8 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Subtract 5z: Subtract 5z from both sides of the equation to isolate the variable z on one side. 3z - 5z = 5z + 8 - 5zSimplify equation: Simplify both sides of the equation. -2z = 8Divide by -2: Divide both sides by -2 to solve for z. z = 8 / -2 z = -4Check solution: Check if the solution z = -4 satisfies the original equation. 3(-4) = 5(-4) + 8 -12 = -20 + 8 -12 ≠ -12

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How many solutions does this equation have? $\newline$ $3z = 5z + 8$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

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Q. How many solutions does this equation have?

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3z = 5z + 8

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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

Subtract $5z$ : Subtract $5z$ from both sides of the equation to isolate the variable $z$ on one side. $\newline$ $3z - 5z = 5z + 8 - 5z$
Simplify equation: Simplify both sides of the equation. $\newline$ $-2z = 8$
Divide by $-2$ : Divide both sides by $-2$ to solve for $z$ . $z = \frac{8}{-2}$ $z = -4$
Check solution: Check if the solution $z = -4$ satisfies the original equation. $3(-4) = 5(-4) + 8$ $-12 = -20 + 8$ $-12 \neq -12$