Example Question - simplify equation
Here are examples of questions we've helped users solve.
Solving Simple Linear Equation
Para resolver la ecuación que se muestra en la imagen, la cual es: \[ \frac{5}{7} = x - 2x \] Primero, buscaremos combinar los términos con x en un lado de la ecuación. Recordemos que \( x - 2x \) es lo mismo que \( 1x - 2x \), lo cual se simplifica a \( -1x \) porque estamos restando 2 veces la x de la x original. Ahora la ecuación se ve así: \[ \frac{5}{7} = -1x \] Para despejar \( x \), necesitamos quitar el coeficiente de -1 que está multiplicando a \( x \). Para hacer eso, podemos dividir ambos lados de la ecuación por -1. \[ -\frac{5}{7} = x \] Entonces, la solución a la ecuación es: \[ x = -\frac{5}{7} \] Hemos encontrado el valor de \( x \) que satisface la ecuación original.
Solving an Equation by Combining Like Terms
To solve the equation \( x + 5 + 6 = 2^3 \), let's first simplify the equation by combining like terms and then solve for \( x \): 1. Combine the constant terms on the left side: \( x + 11 = 2^3 \) 2. Calculate the value of \( 2^3 \): \( 2^3 = 2 \times 2 \times 2 = 8 \) So the equation becomes: \( x + 11 = 8 \) 3. Subtract 11 from both sides to isolate \( x \): \( x + 11 - 11 = 8 - 11 \) \( x = -3 \) Therefore, the solution to the equation is \( x = -3 \).
Solving an Equation with Constants
To solve for \(x\) in the equation given in the image, you first need to simplify the equation: \[x + 5 + 6 = 2^3\] Combine the constant terms on the left-hand side: \[x + 11 = 2^3\] Now, calculate \(2^3\), which is \(2 \times 2 \times 2 = 8\). Replace \(2^3\) with 8 in the equation: \[x + 11 = 8\] Subtract 11 from both sides to solve for \(x\): \[x = 8 - 11\] \[x = -3\] Therefore, \(x = -3\).
Understanding Equation Solving With Like Terms
To solve the equation \( 403s + 1002s = 1410s \), we can combine like terms on the left side by adding the coefficients of \( s \) together. Here's how you do it step by step: 1. Combine like terms (the terms with \( s \)): \[ 403s + 1002s = (403 + 1002)s = 1405s \] 2. Now that we have \( 1405s \) on the left side and \( 1410s \) on the right side, we set them equal to each other: \[ 1405s = 1410s \] 3. In order to find the solution for \( s \), you generally would isolate \( s \) by dividing both sides of the equation by the coefficient of \( s \). However, since the coefficients of \( s \) are equal and there is no constant term, this would result in an identity where any value of \( s \) satisfies the equation. But since the coefficients are actually different (1405 vs. 1410), there seems to be a mistake in the original problem or a transcription error. If the equation were correctly stated as \( 1405s = 1410s \), the only solution would be \( s = 0 \) because that would be the only way the two sides could be equal. Any non-zero value of \( s \) would result in the two sides not being equal. Since the equation you provided is already balanced with \( 403s + 1002s = 1410s \), which simplifies to \( 1405s = 1410s \), this equation has no solution for \( s \) unless there is a mistake in the terms provided. If the equation is correct, then the solution is that there is no value for \( s \) that would satisfy this equation.
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