Example Question - isolating variable in equation
Here are examples of questions we've helped users solve.
Solving an Equation with Addition
The equation shown in the image is: x + (-47.9) = -34.6 To solve for x, you need to move -47.9 to the other side of the equation by adding 47.9 to both sides. Here are the steps: 1. Add 47.9 to both sides of the equation to isolate x on one side: x + (-47.9) + 47.9 = -34.6 + 47.9 2. The -47.9 and +47.9 on the left side will cancel each other out, leaving you with: x = -34.6 + 47.9 3. Now, you simply perform the addition on the right side: x = 13.3 So, the value of x is 13.3.
Solving a Linear Equation with Fractions
The equation provided in the image is: \[ \frac{2}{3} - x + \frac{1}{2} = \frac{x}{2} - 1 \] Let's solve for \( x \). First, we want to combine like terms and get all the \( x \) terms on one side of the equation and the constants on the other side. To do this, it will be easier to work with a common denominator for the fractions. The smallest common denominator for 3 and 2 is 6. Let's convert each fraction to have denominator 6: \[ \frac{2}{3} \cdot \frac{2}{2} = \frac{4}{6} \] \[ \frac{1}{2} \cdot \frac{3}{3} = \frac{3}{6} \] \[ \frac{x}{2} \cdot \frac{3}{3} = \frac{3x}{6} \] Now rewrite the equation with these equivalent fractions: \[ \frac{4}{6} - x + \frac{3}{6} = \frac{3x}{6} - 1 \] Combine the constant fractions on the left side: \[ \frac{4}{6} + \frac{3}{6} = \frac{7}{6} \] Now the equation looks like this: \[ \frac{7}{6} - x = \frac{3x}{6} - 1 \] Add \( x \) to both sides to get all \( x \) terms on the right side: \[ \frac{7}{6} = \frac{3x}{6} + x - 1 \] Recognize that \( x \) is the same as \( \frac{6x}{6} \) and add it to the \( \frac{3x}{6} \): \[ \frac{7}{6} = \frac{3x}{6} + \frac{6x}{6} - 1 \] Combine the \( x \) terms: \[ \frac{7}{6} = \frac{9x}{6} - 1 \] Now we'll solve for \( x \) by isolating it on one side. First, add 1 to both sides to move the constant term to the left side: \[ \frac{7}{6} + 1 = \frac{9x}{6} \] Convert 1 to a fraction with a denominator of 6 to combine it with the \( \frac{7}{6} \): \[ \frac{7}{6} + \frac{6}{6} = \frac{9x}{6} \] Combine the fractions on the left side: \[ \frac{13}{6} = \frac{9x}{6} \] Multiply both sides by \( \frac{6}{9} \) (which is the reciprocal of the coefficient of \( x \)) to isolate \( x \): \[ \frac{13}{6} \cdot \frac{6}{9} = \frac{9x}{6} \cdot \frac{6}{9} \] Simplify: \[ \frac{13}{9} = x \] So, the solution to the equation is: \[ x = \frac{13}{9} \]
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