How many solutions does this equation have? 5/4(x - 1) = 7/2x - 9/4x + 7 Choices: (A)none (B)one (C)two (D)infinitely many

Simplify equation: Simplify the right side of the equation by combining like terms. 5/4(x - 1) = 7/2x - 9/4x + 7 = (14/4x - 9/4x) + 7 = 5/4x + 7Set equal: Set the simplified equation equal to the left side. 5/4(x - 1) = 5/4x + 7Distribute left side: Distribute 5/4 on the left side. 5/4x - 5/4 = 5/4x + 7Subtract to isolate: Subtract 5/4x from both sides to isolate constants. -5/4 = 7

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How many solutions does this equation have? $\newline$ $\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7$ $\newline$ 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

Full solution

Q. How many solutions does this equation have?

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\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7

\newline

Choices:

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(A) none

\newline

(B) one

\newline

\newline

(D) infinitely many

Simplify equation: Simplify the right side of the equation by combining like terms. $\newline$ $\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7$ $\newline$ $= (\frac{14}{4}x - \frac{9}{4}x) + 7$ $\newline$ $= \frac{5}{4}x + 7$
Set equal: Set the simplified equation equal to the left side. $\newline$ $\frac{5}{4}(x - 1) = \frac{5}{4}x + 7$
Distribute left side: Distribute $\frac{5}{4}$ on the left side. $\newline$ $\frac{5}{4}x - \frac{5}{4} = \frac{5}{4}x + 7$
Subtract to isolate: Subtract $\frac{5}{4}x$ from both sides to isolate constants. $\newline$ $-\frac{5}{4} = 7$