How many solutions does this equation have? 4h = 2h − 10 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable h: Subtract 2h from both sides of the equation to isolate the variable h on one side. 4h - 2h = 2h - 2h - 10 Simplifying both sides gives us: 2h = -10Solve for h: Divide both sides of the equation by 2 to solve for h. 2h / 2 = -10 / 2 Simplifying both sides gives us: h = -5Check solution: Check if the solution h = -5 satisfies the original equation. Substitute h with -5 in the original equation: 4(-5) = 2(-5) - 10 -20 = -10 - 10 -20 = -20 Since the left side equals the right side, the solution h = -5 is correct.

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How many solutions does this equation have? $\newline$ $4h = 2h - 10$ $\newline$ 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

Full solution

Q. How many solutions does this equation have?

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4h = 2h - 10

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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 $h$ : Subtract $2h$ from both sides of the equation to isolate the variable $h$ on one side. $\newline$ $4h - 2h = 2h - 2h - 10$ $\newline$ Simplifying both sides gives us: $\newline$ $2h = -10$
Solve for $h$ : Divide both sides of the equation by $2$ to solve for $h$ . $\frac{2h}{2} = \frac{-10}{2}$ Simplifying both sides gives us: $h = -5$
Check solution: Check if the solution $h = -5$ satisfies the original equation. $\newline$ Substitute $h$ with $-5$ in the original equation: $\newline$ $4(-5) = 2(-5) - 10$ $\newline$ $-20 = -10 - 10$ $\newline$ $-20 = -20$ $\newline$ Since the left side equals the right side, the solution $h = -5$ is correct.