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Example Question - isolating variable

Here are examples of questions we've helped users solve.

Solution to Finding the Missing Number in an Equation

To solve for the blank, you need to perform the operation that is inverse to addition, which is subtraction. Take the equation provided: ____ + 7 = -117 Subtract 7 from both sides to isolate the blank: ____ = -117 - 7 ____ = -124 The number that goes into the blank is -124.

Solving for a Variable in a Simple Equation

To solve for the blank, which I'll represent as x, in the equation \( x + 7 = 117 \), you'll need to isolate x on one side of the equation. This can be done by subtracting 7 from both sides of the equation: \( x + 7 - 7 = 117 - 7 \) This simplifies to: \( x = 110 \) Therefore, the number that fits in the blank to make the equation true is 110.

Solving Inequality 5q + 3 < 37

To solve the inequality 5q + 3 < 37, we want to isolate the variable q. We'll do this by first subtracting 3 from both sides of the inequality to eliminate the constant term on the left side: 5q + 3 - 3 < 37 - 3 5q < 34 Next, we'll divide both sides of the inequality by 5 to solve for q: 5q / 5 < 34 / 5 q < 6.8 So we're looking for a value of q that is less than 6.8. Among the options provided: - q = -8 is less than 6.8. - q = -5 is less than 6.8. - q = -2 is less than 6.8. - q = -1 is less than 6.8. All the given options for q are less than 6.8, meaning they all satisfy the inequality 5q + 3 < 37. Therefore, they are all correct solutions to the inequality.

Solving a Linear Equation

La ecuación que se muestra en la imagen es la siguiente: \[ \frac{5x}{3} + x = \frac{2x + 3}{3} \] Para resolver esta ecuación, primero vamos a eliminar el denominador común, multiplicando cada término por 3 para deshacernos de los denominadores: \[ 3 \cdot \left( \frac{5x}{3} \right) + 3 \cdot x = 3 \cdot \left( \frac{2x + 3}{3} \right) \] Simplificamos: \[ 5x + 3x = 2x + 3 \] Ahora, sumamos términos semejantes en ambos lados de la ecuación: \[ 8x = 2x + 3 \] Next, let's isolate the variable x on one side by subtracting 2x from both sides: \[ 8x - 2x = 3 \] \[ 6x = 3 \] Finalmente, dividimos ambos lados de la ecuación por 6 para despejar x: \[ x = \frac{3}{6} \] Esto se simplifica a: \[ x = \frac{1}{2} \] Entonces, la solución a la ecuación es \( x = \frac{1}{2} \) o \( x = 0.5 \).

Solving a Linear Equation Step by Step

Claro, vamos a resolver la ecuación paso a paso. La ecuación original es: \[ 2x - 1 = 5x + 8 \] Primero, queremos despejar \( x \). Para hacerlo, hay que mover los términos con \( x \) a un lado de la ecuación y los términos sin \( x \) al otro lado. Empezaremos restando \( 2x \) de ambos lados de la ecuación para trasladar todos los términos con \( x \) a un lado: \[ 2x - 2x - 1 = 5x - 2x + 8 \] Esto se simplifica a: \[ -1 = 3x + 8 \] Ahora, restaremos 8 de ambos lados de la ecuación para mover el término constante al otro lado: \[ -1 - 8 = 3x + 8 - 8 \] Lo que nos da: \[ -9 = 3x \] Finalmente, dividimos ambos lados por 3 para aislar \( x \): \[ \frac{-9}{3} = \frac{3x}{3} \] Y esto simplifica a: \[ -3 = x \] Por lo tanto, la solución de la ecuación es \( x = -3 \).

Solving an Algebraic Equation Step by Step

Por supuesto, vamos a resolver la ecuación paso a paso. La ecuación dada es: \[ 2(1 + 2x) = 10 \] Primero, distribuimos el 2 que está fuera del paréntesis: \[ 2 \cdot 1 + 2 \cdot 2x = 10 \] \[ 2 + 4x = 10 \] Ahora, vamos a aislar la variable \( x \): Primero, restamos 2 de ambos lados de la ecuación para deshacernos del número que está añadido a \( 4x \): \[ 4x = 10 - 2 \] \[ 4x = 8 \] Finalmente, dividimos ambos lados de la ecuación por 4 para encontrar el valor de \( x \): \[ x = \frac{8}{4} \] \[ x = 2 \] Así que la solución de la ecuación es \( x = 2 \).

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 a Linear Equation

Давайте решим уравнение, представленное на изображении: \( \frac{5}{x - 3} + 27 = \frac{18}{x - 3} \) Чтобы решить это уравнение, нам нужно изолировать переменную \( x \). Так как оба слагаемых с левой и правой стороны уравнения имеют общий знаменатель \( x - 3 \), мы можем исключить его, умножив все части уравнения на \( x - 3 \), чтобы избавиться от дробей. \( (x - 3) \cdot \frac{5}{x - 3} + 27 \cdot (x - 3) = (x - 3) \cdot \frac{18}{x - 3} \) После упрощения мы получим: \( 5 + 27x - 81 = 18 \) Теперь упростим уравнение, сложив члены: \( 27x - 76 = 18 \) Добавим 76 к обеим сторонам уравнения, чтобы перенести константу с левой стороны на правую: \( 27x = 18 + 76 \) \( 27x = 94 \) Теперь разделим обе стороны уравнения на 27, чтобы найти значение \( x \): \( x = \frac{94}{27} \) Таким образом, решение уравнения: \( x = \frac{94}{27} \)

Solving Linear Equation for x

To solve the equation \(0.5x + 0.3 = 9.8\) for \(x\), you need to isolate \(x\) on one side of the equation. You can do this in two steps: 1. Subtract 0.3 from both sides of the equation to move the constant term to the right side: \[0.5x + 0.3 - 0.3 = 9.8 - 0.3\] \[0.5x = 9.5\] 2. Divide both sides of the equation by 0.5 to solve for \(x\): \[\frac{0.5x}{0.5} = \frac{9.5}{0.5}\] \[x = 19\] Therefore, the solution to the equation is \(x = 19\).