Example Question - solve for x
Here are examples of questions we've helped users solve.
Finding the Value of an Angle
<p> Dado que los ángulos de un triángulo suman 180 grados, podemos establecer la siguiente ecuación: </p> <p> 33° + 145° + x = 180° </p> <p> Ahora, sumamos 33° y 145°: </p> <p> 178° + x = 180° </p> <p> A continuación, restamos 178° de ambos lados: </p> <p> x = 180° - 178° </p> <p> Por lo tanto, tenemos: </p> <p> x = 2° </p>
Finding the Value of a Variable
<p>Primero, expandimos cada término en la ecuación:</p> <p>3(x + 2) + 2(x - 3) = 6(x - 5)</p> <p>Esto se convierte en:</p> <p>3x + 6 + 2x - 6 = 6x - 30</p> <p>Combinando términos similares:</p> <p>5x = 6x - 30</p> <p>Ahora, restamos 6x de ambos lados:</p> <p>5x - 6x = -30</p> <p>-x = -30</p> <p>Multiplicamos por -1:</p> <p>x = 30</p>
Find the Original Number in a Simple Algebraic Equation
<p>Seja \( x \) o número desconhecido.</p> <p>A primeira operação é multiplicar \( x \) por 2: \( 2x \).</p> <p>Em seguida, adiciona-se 3 ao produto: \( 2x + 3 \).</p> <p>A soma final é dada como 7: \( 2x + 3 = 7 \).</p> <p>Agora, resolve-se a equação para \( x \):</p> <p>Subtrai-se 3 de ambos os lados da equação: \( 2x = 7 - 3 \).</p> <p>\( 2x = 4 \).</p> <p>Divide-se ambos os lados por 2 para encontrar \( x \): \( x = \frac{4}{2} \).</p> <p>\( x = 2 \).</p> <p>O número desconhecido é 2.</p>
Solving a Rational Equation
<p>Given equation:</p> <p>\(\frac{x}{2} = \frac{5x - 24}{x - 4}\)</p> <p>To solve for \( x \), cross-multiply to eliminate the denominators:</p> <p>\(x(x - 4) = 2(5x - 24)\)</p> <p>Expand both sides:</p> <p>\(x^2 - 4x = 10x - 48\)</p> <p>Move all terms to one side to set the equation to zero:</p> <p>\(x^2 - 4x - 10x + 48 = 0\)</p> <p>Simplify by combining like terms:</p> <p>\(x^2 - 14x + 48 = 0\)</p> <p>Factor the quadratic equation:</p> <p>\((x - 6)(x - 8) = 0\)</p> <p>Set each factor equal to zero:</p> <p>\(x - 6 = 0 \quad \text{or} \quad x - 8 = 0\)</p> <p>Solve for \( x \):</p> <p>\(x = 6 \quad \text{or} \quad x = 8\)</p>
Solving a Linear Equation
<p>\(2x^2 - 10356 = 99800\)</p> <p>Đầu tiên, chúng ta cần chuyển phương trình về dạng chuẩn của phương trình bậc hai:</p> <p>Đưa cả hai vế về cùng một phía:</p> <p>\(2x^2 - 10356 - 99800 = 0\)</p> <p>Giải phương trình bậc hai:</p> <p>\(2x^2 - 110156 = 0\)</p> <p>Chia cả hai vế cho 2:</p> <p>\(x^2 - 55078 = 0\)</p> <p>Thêm 55078 vào cả hai vế:</p> <p>\(x^2 = 55078\)</p> <p>Lấy căn bậc hai cho cả hai vế:</p> <p>\(x = \pm \sqrt{55078}\)</p> <p>Vậy phương trình có hai nghiệm là:</p> <p>\(x = \sqrt{55078}\) hoặc \(x = -\sqrt{55078}\)</p>
Solving a Linear Equation with Distributed Terms
<p>The given equation is:</p> <p>\(\frac{1}{2} (90 + 22x - 10) \cdot 120 = 14,400\).</p> <p>To solve for \(x\), first simplify the equation:</p> <p>Multiply 120 by each term inside the parentheses:</p> <p>\(\frac{1}{2} (120 \cdot 80 + 120 \cdot 22x) = 14,400\)</p> <p>\(\frac{1}{2} (9600 + 2640x) = 14,400\)</p> <p>Multiply both sides by 2 to eliminate the fraction:</p> <p>\(9600 + 2640x = 28,800\)</p> <p>Subtract 9600 from both sides to isolate the \(x\) term:</p> <p>\(2640x = 28,800 - 9600\)</p> <p>\(2640x = 19,200\)</p> <p>Divide both sides by 2640 to solve for \(x\):</p> <p>\(x = \frac{19,200}{2640}\)</p> <p>\(x = 7.2727...\)</p> <p>As an exact fraction, \(x\) equals:</p> <p>\(x = \frac{7}{22}\)</p>
Solve the Linear Equation for the Unknown Variable
<p>Given equation: \( \frac{1}{2} (70 + 2x -10)(20) = \frac{1}{3}600 \)</p> <p>Multiply through by 2 to get rid of the fraction: \( (70 + 2x - 10)(20) = \frac{2}{3}600 \)</p> <p>Simplify inside the parentheses: \( (60 + 2x)(20) = \frac{2}{3}600 \)</p> <p>Multiply out the parentheses: \( 1200 + 40x = \frac{2}{3}600 \)</p> <p>Divide both sides by 40: \( x + 30 = \frac{2}{3} \times 15 \)</p> <p>Divide 600 by 3: \( x + 30 = \frac{2}{3} \times 15 = 2 \times 5 = 10 \)</p> <p>Subtract 30 from both sides: \( x = 10 - 30 \)</p> <p>Therefore: \( x = -20 \)</p>
Logarithmic Equation Problem
<p>\text{已知等式：}\log_3(x + 4) + \log_3(x - 2) = 3.</p> <p>\text{应用对数法则合并同底对数：}\log_3[(x + 4)(x - 2)] = 3.</p> <p>\text{化简等式得：}\log_3(x^2 + 2x - 8) = 3.</p> <p>\text{消去对数得：}x^2 + 2x - 8 = 3^3.</p> <p>\text{解方程：}x^2 + 2x - 8 = 27.</p> <p>x^2 + 2x - 35 = 0.</p> <p>(x + 7)(x - 5) = 0.</p> <p>\text{所以解为：}x = -7 \text{ 或 } x = 5.</p>
Solving a Linear Equation with Variables on Both Sides
<p>Begin by expanding the terms within the parentheses:</p> <p>\[2(3x + 5) - 3(3x - 1) = 3(4 - x)\]</p> <p>\[6x + 10 - 9x + 3 = 12 - 3x\]</p> <p>Combine like terms:</p> <p>\[-3x + 13 = 12 - 3x\]</p> <p>Add \(3x\) to both sides to move variables to one side:</p> <p>\[-3x + 3x + 13 = 12 - 3x + 3x\]</p> <p>\[13 = 12\]</p> <p>Since 13 is not equal to 12, we have an inconsistency. The equation has no solution because it is not an identity, and the two sides of the equation are not equal for any value of \(x\).</p>
Linear Equation Single Variable Problem
<p>\( 6 - 5x = 13 \)</p> <p>\( -5x = 13 - 6 \)</p> <p>\( -5x = 7 \)</p> <p>\( x = -\frac{7}{5} \)</p> <p>\( x = -1.4 \)</p>
Solving the Linear Equation
<p>Given the equation \(4x + 2 = 2(2x + 3)\)</p> <p>First, expand the right-hand side: \(4x + 2 = 4x + 6\)</p> <p>Next, subtract \(4x\) from both sides of the equation: \(4x - 4x + 2 = 4x - 4x + 6\)</p> <p>This simplifies to: \(2 = 6\)</p> <p>Since this result is not possible (\(2\) does not equal \(6\)), the equation has no solution.</p>
Solving a Linear Equation with Fraction
<p>\(\frac{2x + 5}{3} = 11\)</p> <p>Multiply both sides by 3 to eliminate the fraction:</p> <p>\(2x + 5 = 33\)</p> <p>Subtract 5 from both sides:</p> <p>\(2x = 28\)</p> <p>Divide both sides by 2:</p> <p>\(x = 14\)</p>
Exponential Equation Involving Base 5 and 25
<p>Given:</p> <p>\(25^{x-1}=5^{2x-1}-100\)</p> <p>Since \(25\) is a power of \(5\), i.e., \(25 = 5^2\), rewrite the equation:</p> <p>\((5^2)^{x-1}=5^{2x-1}-100\)</p> <p>Apply the exponent product rule \( (a^m)^n = a^{mn} \):</p> <p>\(5^{2(x-1)}=5^{2x-1}-100\)</p> <p>\(5^{2x-2}=5^{2x-1}-100\)</p> <p>Now, set the exponents of base \(5\) equal to each other and solve the resulting equation:</p> <p>\(2x-2=2x-1\)</p> <p>The above equation has no solution for \(x\) since \(2x-2\) cannot equal \(2x-1\). However, since it's a proof that without subtracting the \(100\), the equation would never hold true for any value of \(x\), we may have made an error. Instead, let's look for a different approach to this problem:</p> <p>Let \(y=5^{x-1}\), this gives us the following equation: </p> <p>\(y = 5y - 100\)</p> <p>Solve for \(y\):</p> <p>\(100 = 5y - y\)</p> <p>\(100 = 4y\)</p> <p>\(y = 25\)</p> <p>Substituting back for \(y\):</p> <p>\(5^{x-1} = 25\)</p> <p>Since \(25=5^2\), we have:</p> <p>\(5^{x-1} = 5^2\)</p> <p>Thus, \(x-1 = 2\)</p> <p>Finally, solve for \(x\):</p> <p>\(x = 2 + 1\)</p> <p>\(x = 3\)</p>
Solving a Basic Algebraic Equation for a Variable
<p>To solve the equation \( y(x - 1) = z \) for \( x \), follow these steps:</p> <p>1. Distribute \( y \) into the parentheses: \( yx - y = z \)</p> <p>2. Add \( y \) to both sides of the equation: \( yx = z + y \)</p> <p>3. Divide both sides by \( y \) to isolate \( x \): \( x = \frac{z + y}{y} \)</p>
Solving a Linear Equation with Fractions
To solve the equation in the image, follow these steps: \( \frac{3}{2} - (2x - 8) = 5 - 2(5x - 7) - 5 \) First, distribute the negative sign through the parentheses on the left side: \( \frac{3}{2} - 2x + 8 = 5 - 2(5x - 7) - 5 \) Next, distribute the -2 on the right side: \( \frac{3}{2} - 2x + 8 = 5 - 10x + 14 - 5 \) Combine like terms on the right side: \( \frac{3}{2} - 2x + 8 = 14 - 10x \) Now, to get rid of the fraction on the left side, multiply every term in the equation by 2: \( 2 * \frac{3}{2} - 2 * 2x + 2 * 8 = 2 * 14 - 2 * 10x \) Simplify: \( 3 - 4x + 16 = 28 - 20x \) Now combine like terms on the left side: \( 19 - 4x = 28 - 20x \) Next, we want to get all the x terms on one side and constants on the other. Add 20x to both sides: \( 19 - 4x + 20x = 28 - 20x + 20x \) Simplify: \( 19 + 16x = 28 \) Subtract 19 from both sides to isolate the term with x: \( 19 + 16x - 19 = 28 - 19 \) Simplify: \( 16x = 9 \) Finally, divide by 16 to solve for x: \( x = \frac{9}{16} \) So the solution to the equation is \( x = \frac{9}{16} \).
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