Questions: -3/5 x - 7/10 x + 1/2 x = -56

Transcript text: $-\frac{3}{5} x-\frac{7}{10} x+\frac{1}{2} x=-56$

Solution

Solution Steps

To solve the equation $-\frac{3}{5} x - \frac{7}{10} x + \frac{1}{2} x = -56$, we need to combine the like terms on the left side of the equation. This involves finding a common denominator for the fractions, combining them, and then solving for $x$.

Step 1: Combine Like Terms

The given equation is:

\[ -\frac{3}{5} x - \frac{7}{10} x + \frac{1}{2} x = -56 \]

To combine the like terms, we first find a common denominator for the fractions. The common denominator for 5, 10, and 2 is 10. Rewriting each term with this common denominator, we have:

\[ -\frac{6}{10} x - \frac{7}{10} x + \frac{5}{10} x \]

Combine these terms:

\[ \left(-\frac{6}{10} - \frac{7}{10} + \frac{5}{10}\right) x = -\frac{8}{10} x = -0.8x \]

Step 2: Solve for $x$

The equation now simplifies to:

\[ -0.8x = -56 \]

To solve for $x$, divide both sides by $-0.8$:

\[ x = \frac{-56}{-0.8} = 70 \]