Solve for x and write your answer in simplest form. -3x-(3)/(2)(-5x+1)=(1)/(2)(-x-(1)/(2))-5 Answer: x=

Write Equation: Write down the original equation. -3x - (3/2)(-5x + 1) = (1/2)(-x - (1/2)) - 5Distribute Fractions: Distribute the fractions on both sides of the equation. -3x - (3/2)(-5x) - (3/2)(1) = (1/2)(-x) - (1/2)(1/2) - 5Simplify Terms: Simplify the distributed terms. -3x + (15/2)x - 3/2 = -1/2x - 1/4 - 5Combine Like Terms: Combine like terms and simplify the right side of the equation. -3x + (15/2)x - 3/2 = -1/2x - 1/4 - 20/4 -3x + (15/2)x - 3/2 = -1/2x - 21/4Convert to Common Denominator: Combine like terms on the right side of the equation. -3x + (15/2)x - 3/2 = -1/2x - 21/4Combine X Terms: Convert -3x to a fraction with a common denominator of 2 to combine with (15/2)x. -6/2x + (15/2)x - 3/2 = -1/2x - 21/4Add/Subtract X Terms: Combine the x terms on the left side of the equation. (15/2 - 6/2)x - 3/2 = -1/2x - 21/4 (9/2)x - 3/2 = -1/2x - 21/4Isolate X Term: Add 1/2x to both sides of the equation to get all x terms on one side. (9/2)x + 1/2x - 3/2 = -21/4Combine Fractions: Combine the x terms on the left side of the equation. (9/2 + 1/2)x - 3/2 = -21/4 (10/2)x - 3/2 = -21/4 5x - 3/2 = -21/4Solve for X: Convert -3/2 to a fraction with a common denominator of 4 to combine with -21/4. 5x - 6/4 = -21/4Divide by 5: Add 6/4 to both sides of the equation to isolate the x term. 5x = -21/4 + 6/4Multiply Fractions: Combine the fractions on the right side of the equation. 5x = -15/4Simplify Fraction: Divide both sides by 5 to solve for x. x = (-15/4) / 5 x = (-15/4) * (1/5)Multiply the fractions to find the value of x. x = -15/20Simplify the fraction to its simplest form. x = -3/4

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Solve for
x and write your answer in simplest form.

-3x-(3)/(2)(-5x+1)=(1)/(2)(-x-(1)/(2))-5
Answer:
x=

Solve for $x$ and write your answer in simplest form. $\newline$ $-3 x-\frac{3}{2}(-5 x+1)=\frac{1}{2}\left(-x-\frac{1}{2}\right)-5$ $\newline$ Answer: $x=$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Solve for

x

and write your answer in simplest form.

\newline

-3 x-\frac{3}{2}(-5 x+1)=\frac{1}{2}\left(-x-\frac{1}{2}\right)-5

\newline

Answer:

x=

Write Equation: Write down the original equation. $\newline$ \(-3x - \left(\frac{ $3$ }{ $2$ }\right)( $-5$ x + $1$ ) = \left(\frac{ $1$ }{ $2$ }\right)(-x - \left(\frac{ $1$ }{ $2$ }\right)) - $5$
Distribute Fractions: Distribute the fractions on both sides of the equation. $\newline$ \(-3x - \left(\frac{ $3$ }{ $2$ }\right)( $-5$ x) - \left(\frac{ $3$ }{ $2$ }\right)( $1$ ) = \left(\frac{ $1$ }{ $2$ }\right)(-x) - \left(\frac{ $1$ }{ $2$ }\right)\left(\frac{ $1$ }{ $2$ }\right) - $5$
Simplify Terms: Simplify the distributed terms. $\newline$ $-3x + \left(\frac{15}{2}\right)x - \frac{3}{2} = -\frac{1}{2}x - \frac{1}{4} - 5$
Combine Like Terms: Combine like terms and simplify the right side of the equation. $\newline$ $-3x + \left(\frac{15}{2}\right)x - \frac{3}{2} = -\frac{1}{2}x - \frac{1}{4} - \frac{20}{4}$ $\newline$ $-3x + \left(\frac{15}{2}\right)x - \frac{3}{2} = -\frac{1}{2}x - \frac{21}{4}$
Convert to Common Denominator: Combine like terms on the right side of the equation. $\newline$ $-3x + \left(\frac{15}{2}\right)x - \frac{3}{2} = -\frac{1}{2}x - \frac{21}{4}$
Combine $X$ Terms: Convert $-3x$ to a fraction with a common denominator of $2$ to combine with $(\frac{15}{2})x$ . $\newline$ $-\frac{6}{2}x + (\frac{15}{2})x - \frac{3}{2} = -\frac{1}{2}x - \frac{21}{4}$
Add/Subtract X Terms: Combine the x terms on the left side of the equation. $\newline$ $(\frac{15}{2} - \frac{6}{2})x - \frac{3}{2} = -\frac{1}{2}x - \frac{21}{4}$ $\newline$ $(\frac{9}{2})x - \frac{3}{2} = -\frac{1}{2}x - \frac{21}{4}$
Isolate X Term: Add $\frac{1}{2}x$ to both sides of the equation to get all x terms on one side. $\newline$ $(\frac{9}{2})x + \frac{1}{2}x - \frac{3}{2} = -\frac{21}{4}$
Combine Fractions: Combine the $x$ terms on the left side of the equation. $\newline$ $(\frac{9}{2} + \frac{1}{2})x - \frac{3}{2} = -\frac{21}{4}$ $\newline$ $(\frac{10}{2})x - \frac{3}{2} = -\frac{21}{4}$ $\newline$ $5x - \frac{3}{2} = -\frac{21}{4}$
Solve for X: Convert $-\frac{3}{2}$ to a fraction with a common denominator of $4$ to combine with $-\frac{21}{4}$ . $\newline$ $5x - \frac{6}{4} = -\frac{21}{4}$
Divide by $5$ : Add $\frac{6}{4}$ to both sides of the equation to isolate the $x$ term. $\newline$ $5x = -\frac{21}{4} + \frac{6}{4}$
Multiply Fractions: Combine the fractions on the right side of the equation. $\newline$ $5x = -\frac{15}{4}$
Simplify Fraction: Divide both sides by $5$ to solve for $x$ . $x = \frac{-15}{4} / 5$ $x = \frac{-15}{4} \cdot \frac{1}{5}$
Simplify Fraction: Divide both sides by $5$ to solve for $x$ . $x = \frac{-15}{4} / 5$ $x = \frac{-15}{4} \cdot \frac{1}{5}$ Multiply the fractions to find the value of $x$ . $x = \frac{-15}{20}$
Simplify Fraction: Divide both sides by $5$ to solve for $x$ . $x = (-15/4) / 5$ $x = (-15/4) \times (1/5)$ Multiply the fractions to find the value of $x$ . $x = -15/20$ Simplify the fraction to its simplest form. $x = -3/4$