Solve for x and write your answer in simplest form. -9-2x=4((1)/(2)x+1)+(3)/(2) Answer: x=

Distribute and Simplify: First, distribute the 4 on the right side of the equation to both terms inside the parentheses. -9 - 2x = 4 * (1/2)x + 4 * 1 + (3/2)Combine Like Terms: Now, simplify the right side of the equation by performing the multiplication. -9 - 2x = 2x + 4 + (3/2)Isolate x Terms: Combine like terms on the right side by adding 4 and (3/2). -9 - 2x = 2x + (8/2) + (3/2) -9 - 2x = 2x + (11/2)Clear Denominator: To isolate the x terms on one side, add 2x to both sides of the equation. -9 = 4x + (11/2)Subtract to Isolate x: Now, to get rid of the fraction, multiply every term by 2 to clear the denominator. -18 = 8x + 11Divide to Solve x: Subtract 11 from both sides to isolate the term with x. -18 - 11 = 8x -29 = 8xFinally, divide both sides by 8 to solve for x. x = -29 / 8

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Math Problems

Algebra 2

Simplify variable expressions using properties

Full solution

Q. Solve for

x

and write your answer in simplest form.

\newline

-9-2 x=4\left(\frac{1}{2} x+1\right)+\frac{3}{2}

\newline

Answer:

x=

Distribute and Simplify: First, distribute the $4$ on the right side of the equation to both terms inside the parentheses. $-9 - 2x = 4 \times (\frac{1}{2})x + 4 \times 1 + (\frac{3}{2})$
Combine Like Terms: Now, simplify the right side of the equation by performing the multiplication. $\newline$ $-9 - 2x = 2x + 4 + \left(\frac{3}{2}\right)$
Isolate x Terms: Combine like terms on the right side by adding $4$ and $(3/2)$ . $\newline$ $-9 - 2x = 2x + (8/2) + (3/2)$ $\newline$ $-9 - 2x = 2x + (11/2)$
Clear Denominator: To isolate the $x$ terms on one side, add $2x$ to both sides of the equation. $\newline$ $-9 = 4x + \left(\frac{11}{2}\right)$
Subtract to Isolate $x$ : Now, to get rid of the fraction, multiply every term by $2$ to clear the denominator. $\newline$ $-18 = 8x + 11$
Divide to Solve $x$ : Subtract $11$ from both sides to isolate the term with $x$ .
$-18 - 11 = 8x$
$-29 = 8x$
Divide to Solve $x$ : Subtract $11$ from both sides to isolate the term with $x$ .
$-18 - 11 = 8x$
$-29 = 8x$ Finally, divide both sides by $8$ to solve for $x$ .
$x = -\frac{29}{8}$