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consider this equation

5/8(x + 1/2) = 100

5 answers

To solve the equation \( \frac{5}{8}(x + \frac{1}{2}) = 100 \), follow these steps:

  1. Isolate the term involving \( x \): \[ x + \frac{1}{2} = 100 \cdot \frac{8}{5} \]

  2. Calculate \( 100 \cdot \frac{8}{5} \): \[ 100 \cdot \frac{8}{5} = 100 \cdot 1.6 = 160 \] So, the equation simplifies to: \[ x + \frac{1}{2} = 160 \]

  3. Subtract \( \frac{1}{2} \) from both sides: \[ x = 160 - \frac{1}{2} \] To perform the subtraction, convert \( 160 \) to a fraction: \[ 160 = \frac{320}{2}, \ \text{so} \ x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2} \]

Thus, the solution to the equation is: \[ x = \frac{319}{2} \quad \text{or} \quad x = 159.5 \]

what do you mean by isolate the term using x

When I mentioned "isolate the term involving \( x \)," I meant the process of rearranging the equation so that the variable \( x \) is on one side of the equation by itself. This is a common step in solving equations, allowing you to find the value of the variable.

Here's a clearer breakdown of that step in the context of your equation \( \frac{5}{8}(x + \frac{1}{2}) = 100 \):

  1. Distribute/Multiply: The first step involves dealing with the fraction by multiplying both sides by the reciprocal to eliminate the fraction. Here, we can multiply both sides by \( \frac{8}{5} \) to make it simpler: \[ (x + \frac{1}{2}) = 100 \cdot \frac{8}{5} \]

  2. Calculate the right side: \[ 100 \cdot \frac{8}{5} = 160 \] So now, we have: \[ x + \frac{1}{2} = 160 \]

  3. Isolate \( x \): Now, we move \( \frac{1}{2} \) to the other side by subtracting: \[ x = 160 - \frac{1}{2} \]

  4. Perform the subtraction: Convert \( 160 \) into a fraction to make the subtraction easier: \[ x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2} \]

The goal of isolating \( x \) is to get an equation where \( x \) is alone on one side, which leads us to find its value clearly. In summary, isolating the variable helps us solve for it directly.

its only 2 steps so what should I do

I understand that you may be looking for a more straightforward solution without getting into detailed explanations. Let's simplify the steps for solving the equation \( \frac{5}{8}(x + \frac{1}{2}) = 100 \).

Here’s how to solve it in just a couple of steps:

Step 1: Eliminate the Fraction

Multiply both sides of the equation by \( \frac{8}{5} \) to eliminate the fraction: \[ x + \frac{1}{2} = 100 \cdot \frac{8}{5} \]

Calculate: \[ 100 \cdot \frac{8}{5} = 160 \]

So, the equation becomes: \[ x + \frac{1}{2} = 160 \]

Step 2: Solve for \( x \)

Now, subtract \( \frac{1}{2} \) from both sides: \[ x = 160 - \frac{1}{2} \]

Convert \( 160 \) to a fraction: \[ x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2} \]

Thus, the solution is: \[ x = \frac{319}{2} \quad \text{or} \quad x = 159.5 \]

That's it! In two concise steps, you've solved the equation. If you have any further questions or need more clarifications, feel free to ask!