Example Question - solve equations
Here are examples of questions we've helped users solve.
Solving Algebraic Equations
<p>Для решения уравнений вида \(\frac{x}{a} = b\) и \(\frac{m}{n} = c\), где \(x, m, n, a, b, c\) - числа, нужно выполнить следующие шаги:</p> <p>а) \(\frac{x}{9} = 13\)</p> <p>Шаг 1: Умножьте обе части уравнения на 9.</p> <p>\(x = 13 \times 9\)</p> <p>\(x = 117\)</p> <p>б) \(\frac{132}{k} = 11\)</p> <p>Шаг 1: Умножьте обе части уравнения на \(k\).</p> <p>132 = 11k</p> <p>Шаг 2: Разделите обе части уравнения на 11.</p> <p>\(k = \frac{132}{11}\)</p> <p>\(k = 12\)</p> <p>в) \(\frac{m}{12} = 28\)</p> <p>Шаг 1: Умножьте обе части уравнения на 12.</p> <p>\(m = 28 \times 12\)</p> <p>\(m = 336\)</p> <p>г) \(\frac{528}{n} = 66\)</p> <p>Шаг 1: Умножьте обе части уравнения на \(n\).</p> <p>528 = 66n</p> <p>Шаг 2: Разделите обе части уравнения на 66.</p> <p>\(n = \frac{528}{66}\)</p> <p>\(n = 8\)</p>
Step-by-Step Equation Solving
Por supuesto, vamos a resolver la ecuación paso a paso. La ecuación que nos has dado es: \[ 2x - 1 = 5x + 8 \] Para resolver la ecuación, primero queremos despejar la variable \( x \) en uno de los lados de la ecuación. Hagámoslo restando \( 2x \) en ambos lados y también restando \( 8 \) en ambos lados para aislar \( x \). Así que tenemos: Restamos \( 2x \) de ambos lados y obtenemos: \[ -1 = 3x + 8 \] Ahora, restamos \( 8 \) de ambos lados y obtenemos: \[ -1 - 8 = 3x \] \[ -9 = 3x \] Finalmente, dividimos ambos lados entre 3 para despejar \( x \): \[ \frac{-9}{3} = x \] \[ x = -3 \] La solución a la ecuación es \( x = -3 \).
Solving Exponential Equation with Substitution
The image shows an equation: \[e^{2x} - 4 \cdot 2^x + 4 = 0\] To solve this equation, let's apply a substitution. Notice that the terms \(e^{2x}\) and \(2^x\) suggest that we can set \(u = 2^x\). Then \(e^{2x} = (e^x)^2 = (2^x)^2 = u^2\). Our equation now becomes: \[u^2 - 4u + 4 = 0\] Now, factor this quadratic equation: \[(u - 2)^2 = 0\] Solving for \(u\), we get \(u = 2\). Since we set \(u = 2^x\), we now have: \[2^x = 2\] Taking the logarithm base 2 of both sides gives: \[x \cdot \log_2(2) = \log_2(2)\] \[\Rightarrow x = 1\] So, the solution to the equation is \(x = 1\).
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