Solve for all values of x : 3x(5x-1)-5(5x-1)=0 Answer: x=

Factor out common expression: First, notice that the expression (5x-1) is common to both terms on the left side of the equation. We can factor it out. 3x(5x-1) - 5(5x-1) = (5x-1)(3x-5)Apply zero product property: Now that we have factored the equation, we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero: 5x - 1 = 0 or 3x - 5 = 0Solve for x in first equation: Solve the first equation 5x - 1 = 0 for x. Add 1 to both sides: 5x = 1 Now divide by 5: x = 1/5Solve for x in second equation: Solve the second equation 3x - 5 = 0 for x. Add 5 to both sides: 3x = 5 Now divide by 3: x = 5/3

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Solve for all values of
x :

3x(5x-1)-5(5x-1)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $3 x(5 x-1)-5(5 x-1)=0$ $\newline$ Answer: $x=$

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Math Problems

Algebra 1

Solve multi-step linear equations

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Q. Solve for all values of

x

\newline

3 x(5 x-1)-5(5 x-1)=0

\newline

Answer:

x=

Factor out common expression: First, notice that the expression $(5x-1)$ is common to both terms on the left side of the equation. We can factor it out. $3x(5x-1) - 5(5x-1) = (5x-1)(3x-5)$
Apply zero product property: Now that we have factored the equation, we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero: $\newline$ $5x - 1 = 0$ or $3x - 5 = 0$
Solve for x in first equation: Solve the first equation $5x - 1 = 0$ for x. $\newline$ Add $1$ to both sides: $\newline$ $5x = 1$ $\newline$ Now divide by $5$ : $\newline$ $x = \frac{1}{5}$
Solve for x in second equation: Solve the second equation $3x - 5 = 0$ for x. $\newline$ Add $5$ to both sides: $\newline$ $3x = 5$ $\newline$ Now divide by $3$ : $\newline$ $x = \frac{5}{3}$