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Solve the following equation for
x. Express your answer in the simplest form.

-5x-(1)/(2)(6x+8)=-7x+8(5x-5)

Solve the following equation for $x$ . Express your answer in the simplest form. $\newline$ $-5 x-\frac{1}{2}(6 x+8)=-7 x+8(5 x-5)$ $\newline$

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Simplify radical expressions using the distributive property

Full solution

Q. Solve the following equation for

x

. Express your answer in the simplest form.

\newline

-5 x-\frac{1}{2}(6 x+8)=-7 x+8(5 x-5)

\newline

Distribute and Simplify: First, distribute the $-\frac{1}{2}$ across the $(6x + 8)$ . $\newline$ $-5x - \left(\frac{1}{2}\right)6x - \left(\frac{1}{2}\right)8 = -7x + 8\cdot5x - 8\cdot5$
Combine Like Terms: Simplify the distributed terms. $\newline$ $-5x - 3x - 4 = -7x + 40x - 40$
Add/Subtract Terms: Combine like terms on both sides. $\newline$ $-8x - 4 = 33x - 40$
Isolate x Term: Add $8x$ to both sides to get the x terms on one side. $\newline$ $-8x + 8x - 4 = 33x + 8x - 40$
Add/Subtract to Isolate $x$ : Simplify the equation after adding $8x$ to both sides. $\newline$ $-4 = 41x - 40$
Simplify Equation: Add $40$ to both sides to isolate the $x$ term. $\newline$ $-4 + 40 = 41x - 40 + 40$
Add/Subtract to Isolate $x$ : Simplify the equation after adding $40$ to both sides. $\newline$ $36 = 41x$
Simplify Equation: Divide both sides by $41$ to solve for $x$ . $\newline$ $\frac{36}{41} = \frac{41x}{41}$
Divide to Solve for x: Simplify the equation after dividing by $41$ . $x = \frac{36}{41}$

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