Solve for $x$.
$$
-\frac{8}{x+3}=-\frac{5}{2 x+6}+2
$$

If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Question

Solve for $x$.
$$
-\frac{8}{x+3}=-\frac{5}{2 x+6}+2
$$

If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Start by simplifying the given equation: $$ -\frac{8}{x+3} = -\frac{5}{2x+6} + 2 $$ Notice that $2x + 6$ can be rewritten as $2(x + 3)$. ‖ ‖ step 2 ⋮ Rewrite the equation using the substitution $2(x + 3)$: $$ -\frac{8}{x+3} = -\frac{5}{2(x+3)} + 2 $$ This simplifies to: $$ -\frac{8}{x+3} = -\frac{5}{2(x+3)} + 2 $$ ‖ ‖ step 3 ⋮ To eliminate the fractions, multiply both sides by $2(x+3)$: $$ -8 \cdot 2 = -5 + 2 \cdot 2(x+3) \cdot (x+3) $$ This simplifies to: $$ -16 = -5 + 4(x+3) $$ ‖ ‖ step 4 ⋮ Simplify the equation: $$ -16 = -5 + 4(x+3) $$ Add 5 to both sides: $$ -11 = 4(x+3) $$ ‖ ‖ step 5 ⋮ Divide both sides by 4: $$ -\frac{11}{4} = x + 3 $$ Subtract 3 from both sides: $$ x = -\frac{11}{4} - 3 $$ Simplify the right-hand side: $$ x = -\frac{11}{4} - \frac{12}{4} = -\frac{23}{4} $$ ‖ ∻Answer∻ ⚹ $x = -\frac{23}{4}$ ⚹ ∻Key Concept∻ ⚹Solving rational equations⚹ ∻Explanation∻ ⚹To solve rational equations, it is often helpful to eliminate the fractions by multiplying through by a common denominator. This simplifies the equation and makes it easier to solve for the variable.⚹◊What are the steps to solve the equation $- \frac{8}{x+3} = - \frac{5}{2x+6} + 2$ for $x$?⍭ Generate me a similar question◊

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