(x)/(x+3)=(x+2)/(x+6:2) Fid x

Simplify Equation: First, let's simplify the equation by getting rid of the colon, which represents division. The equation (x+6:2) can be simplified to (x+6)/2.Cross-Multiply Fractions: Now, we have the equation (x)/(x+3) = (x+2)/((x+6)/2). To solve for x, we need to cross-multiply to get rid of the fractions.Expand Equations: Cross-multiplying gives us 2x * (x+3) = (x+2) * (x+6).Rearrange Terms: Expanding both sides of the equation, we get 2x^2 + 6x = x^2 + 8x + 12.Combine Like Terms: Now, let's move all terms to one side of the equation to set it equal to zero. Subtract x^2 from both sides and subtract 8x from both sides to get 2x^2 + 6x - x^2 - 8x = 12.Factor Quadratic Equation: Simplify the equation by combining like terms to get x^2 - 2x - 12 = 0.Set Factors Equal: Now we need to factor the quadratic equation. The factors of -12 that add up to -2 are -6 and +4. So we can write the equation as (x - 6)(x + 4) = 0.Solve for x: Setting each factor equal to zero gives us the possible solutions for x: x - 6 = 0 or x + 4 = 0.Solving each equation for x gives us x = 6 or x = -4.

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Math Problems

Grade 7

Add three or more integers

Full solution

\frac{x}{x+3}=\frac{x+2}{x+\frac{6}{2}}

Find `x`

Simplify Equation: First, let's simplify the equation by getting rid of the colon, which represents division. The equation $(x+6:2)$ can be simplified to $(x+6)/2$ .
Cross-Multiply Fractions: Now, we have the equation (\frac{x}{x+3} = \frac{x+2}{\frac{x+6}{2}})\. To solve for \$x, we need to cross-multiply to get rid of the fractions.
Expand Equations: Cross-multiplying gives us $2x \times (x+3) = (x+2) \times (x+6)$ .
Rearrange Terms: Expanding both sides of the equation, we get $2x^2 + 6x = x^2 + 8x + 12$ .
Combine Like Terms: Now, let's move all terms to one side of the equation to set it equal to zero. Subtract $x^2$ from both sides and subtract $8x$ from both sides to get $2x^2 + 6x - x^2 - 8x = 12$ .
Factor Quadratic Equation: Simplify the equation by combining like terms to get $x^2 - 2x - 12 = 0$ .
Set Factors Equal: Now we need to factor the quadratic equation. The factors of $-12$ that add up to $-2$ are $-6$ and $+4$ . So we can write the equation as $(x - 6)(x + 4) = 0$ .
Solve for $x$ : Setting each factor equal to zero gives us the possible solutions for $x$ : $x - 6 = 0$ or $x + 4 = 0$ .
Solve for x: Setting each factor equal to zero gives us the possible solutions for x: $x - 6 = 0$ or $x + 4 = 0$ . Solving each equation for x gives us $x = 6$ or $x = -4$ .