How many solutions does this equation have? 8/9x - 1/3x + 4 = 5/9(x + 2) Choices: (A)none (B)one (C)two (D)infinitely many

Combine like terms: Combine like terms on the left side of the equation. 8/9x - 1/3x can be simplified by finding a common denominator, which is 9. 8/9x - 3/9x = 5/9x. So, the equation becomes 5/9x + 4 = 5/9(x + 2).Distribute on right side: Distribute 5/9 on the right side of the equation. 5/9(x + 2) = 5/9x + 10/9. Now, the equation is 5/9x + 4 = 5/9x + 10/9.Subtract to isolate constants: Subtract 5/9x from both sides to isolate the constants. 5/9x + 4 - 5/9x = 5/9x + 10/9 - 5/9x. This simplifies to 4 = 10/9.

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How many solutions does this equation have? $\newline$ $\frac{8}{9}x - \frac{1}{3}x + 4 = \frac{5}{9}(x + 2)$ $\newline$ Choices: $\newline$ (A) none $\newline$ (B) one $\newline$ (C) two $\newline$ (D) infinitely many

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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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\frac{8}{9}x - \frac{1}{3}x + 4 = \frac{5}{9}(x + 2)

\newline

Choices:

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(A) none

\newline

(B) one

\newline

\newline

(D) infinitely many

Combine like terms: Combine like terms on the left side of the equation. $\newline$ $\frac{8}{9}x - \frac{1}{3}x$ can be simplified by finding a common denominator, which is $9$ . $\newline$ $\frac{8}{9}x - \frac{3}{9}x = \frac{5}{9}x$ . $\newline$ So, the equation becomes $\frac{5}{9}x + 4 = \frac{5}{9}(x + 2)$ .
Distribute on right side: Distribute $\frac{5}{9}$ on the right side of the equation. $\newline$ $\frac{5}{9}(x + 2) = \frac{5}{9}x + \frac{10}{9}$ . $\newline$ Now, the equation is $\frac{5}{9}x + 4 = \frac{5}{9}x + \frac{10}{9}$ .
Subtract to isolate constants: Subtract $\frac{5}{9}x$ from both sides to isolate the constants. $\newline$ $\frac{5}{9}x + 4 - \frac{5}{9}x = \frac{5}{9}x + \frac{10}{9} - \frac{5}{9}x$ . $\newline$ This simplifies to $4 = \frac{10}{9}$ .