Question

Solve equation for the unknown quantity. Check your answers. \(x+4=2 \frac{1}{2}\)

Short answer

Answer: \(x = \frac{-3}{2}\)

Step-by-step solution

Rewrite the mixed number as an improper fraction

To work with the given equation, let's first rewrite the mixed number \(2\frac{1}{2}\) as an improper fraction. We do this by multiplying the whole number (2) by the denominator (2) and adding the numerator (1). Then, the result becomes the new numerator, and the denominator remains the same. \(2\frac{1}{2} = \frac{2 × 2 + 1}{2} = \frac{5}{2}\) So, the equation becomes: \(x + 4 = \frac{5}{2}\)

Isolate x by subtracting 4 from both sides

Now, we need to isolate x by subtracting 4 from both sides of the equation. In order to do this, we need to rewrite 4 as a fraction with a denominator of 2 so that we can combine it with \(\frac{5}{2}\). \(4 = \frac{4 × 2}{2} = \frac{8}{2}\) Now, we can subtract \(\frac{8}{2}\) from both sides, as follows: \(x = \frac{5}{2} - \frac{8}{2}\)

Subtract the fractions

Since the fractions have the same denominator, we can subtract their numerators and keep the denominator unchanged: \(x = \frac{5 - 8}{2} = \frac{-3}{2}\) So, we have found the value of x: \(x = \frac{-3}{2}\)

Check the result

Let's check if our solution is correct by substituting the value of x back into the original equation: \(\frac{-3}{2} + 4 = 2\frac{1}{2}\) First, we need to rewrite 4 as a fraction with a denominator of 2: \(4 = \frac{8}{2}\) Now, we can add the fractions: \(\frac{-3}{2} + \frac{8}{2} = \frac{-3 + 8}{2} = \frac{5}{2} = 2\frac{1}{2}\) Since both sides of the equation are equal, our solution is correct. Therefore, the final answer is: \(x = \frac{-3}{2}\)