(-5x/2 -1/4)8 = -x/2 +1

Distribute 8 to terms: We need to distribute 8 to both terms in the parentheses on the left side of the equation. (-5x/2 - 1/4) * 8 = -x/2 + 1 Distribute 8 to -5x/2 and -1/4 separately. (-5x/2) * 8 + (-1/4) * 8 = -x/2 + 1Simplify multiplication: Simplify the multiplication. (-5x/2) * 8 = -5x * 4 = -20x (-1/4) * 8 = -2 So, the left side of the equation becomes -20x - 2. -20x - 2 = -x/2 + 1Isolate variable x: Now we need to isolate the variable x on one side of the equation. Let's move all terms containing x to the left side and constants to the right side. Add 20x to both sides and add 2 to both sides. -20x - 2 + 20x + 2 = -x/2 + 1 + 20x + 2Combine like terms: Simplify both sides of the equation. The x terms on the left side cancel each other out, and we are left with 0 on the left side. 0 = -x/2 + 20x + 3Simplify x terms: Combine like terms on the right side of the equation. Since -x/2 is the same as -0.5x, we can combine it with 20x. 0 = -0.5x + 20x + 3Subtract to isolate x: Simplify the x terms. -0.5x + 20x = 19.5x 0 = 19.5x + 3Simplify both sides: Subtract 3 from both sides to isolate the x term. 0 - 3 = 19.5x + 3 - 3Divide to solve for x: Simplify both sides of the equation. -3 = 19.5xFind value of x: Divide both sides by 19.5 to solve for x. -3 / 19.5 = 19.5x / 19.5Simplify the division to find the value of x. x = -3 / 19.5 x = -0.15384615384615385

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

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Algebra 2

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

Distribute $8$ to terms: We need to distribute $8$ to both terms in the parentheses on the left side of the equation. $\newline$ $(-\frac{5x}{2} - \frac{1}{4}) \times 8 = -\frac{x}{2} + 1$ $\newline$ Distribute $8$ to $-\frac{5x}{2}$ and $-\frac{1}{4}$ separately. $\newline$ $(-\frac{5x}{2}) \times 8 + (-\frac{1}{4}) \times 8 = -\frac{x}{2} + 1$
Simplify multiplication: Simplify the multiplication. $\newline$ $(-\frac{5x}{2}) \times 8 = -5x \times 4 = -20x$ $\newline$ $(-\frac{1}{4}) \times 8 = -2$ $\newline$ So, the left side of the equation becomes $-20x - 2$ . $\newline$ $-20x - 2 = -\frac{x}{2} + 1$
Isolate variable x: Now we need to isolate the variable x on one side of the equation. Let's move all terms containing x to the left side and constants to the right side. $\newline$ Add $20x$ to both sides and add $2$ to both sides. $\newline$ $-20x - 2 + 20x + 2 = -\frac{x}{2} + 1 + 20x + 2$
Combine like terms: Simplify both sides of the equation. $\newline$ The $x$ terms on the left side cancel each other out, and we are left with $0$ on the left side. $\newline$ $0 = -\frac{x}{2} + 20x + 3$
Simplify $x$ terms: Combine like terms on the right side of the equation. $\newline$ Since $-\frac{x}{2}$ is the same as $-0.5x$ , we can combine it with $20x$ . $\newline$ $0 = -0.5x + 20x + 3$
Subtract to isolate x: Simplify the x terms. $\newline$ $-0.5x + 20x = 19.5x$ $\newline$ $0 = 19.5x + 3$
Simplify both sides: Subtract $3$ from both sides to isolate the $x$ term. $\newline$ $0 - 3 = 19.5x + 3 - 3$
Divide to solve for x: Simplify both sides of the equation. $\newline$ $-3 = 19.5x$
Find value of x: Divide both sides by $19.5$ to solve for $x$ . $\newline$ $-\frac{3}{19.5} = \frac{19.5x}{19.5}$
Find value of x: Divide both sides by $19.5$ to solve for $x$ .
$\frac{-3}{19.5} = \frac{19.5x}{19.5}$ Simplify the division to find the value of $x$ .
$x = \frac{-3}{19.5}$
$x = -0.15384615384615385$