How many solutions does this equation have? 6t = –6 + 4t Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable t: Isolate the variable t on one side of the equation. To do this, we subtract 4t from both sides of the equation. 6t - 4t = –6 + 4t - 4t This simplifies to: 2t = -6Solve for t: Solve for t by dividing both sides of the equation by 2. 2t / 2 = -6 / 2 This simplifies to: t = -3Check solution t=-3: Check if the solution t = -3 satisfies the original equation. Substitute t with -3 in the original equation: 6(-3) = –6 + 4(-3) -18 = -6 - 12 -18 = -18 Since both sides of the equation are equal, the solution t = -3 is correct.

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How many solutions does this equation have? $\newline$ $6t = -6 + 4t$ $\newline$ 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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6t = -6 + 4t

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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

Isolate variable t: Isolate the variable t on one side of the equation. $\newline$ To do this, we subtract $4t$ from both sides of the equation. $\newline$ $6t - 4t = -6 + 4t - 4t$ $\newline$ This simplifies to: $\newline$ $2t = -6$
Solve for t: Solve for t by dividing both sides of the equation by $2$ . $\newline$ $\frac{2t}{2} = \frac{-6}{2}$ $\newline$ This simplifies to: $\newline$ $t = -3$
Check solution $t=-3$ : Check if the solution $t = -3$ satisfies the original equation. $\newline$ Substitute $t$ with $-3$ in the original equation: $\newline$ $6(-3) = –6 + 4(-3)$ $\newline$ $-18 = -6 - 12$ $\newline$ $-18 = -18$ $\newline$ Since both sides of the equation are equal, the solution $t = -3$ is correct.