7 answers
To solve the equation \( x - 78 = -5 \), you can add a number to both sides to isolate \( x \).
First, let's determine what number should be added. We want to get rid of the \(-78\) on the left side, so we can add \(78\) to both sides:
\[ x - 78 + 78 = -5 + 78 \]
This simplifies to:
\[ x = 73 \]
Thus, the number that should be added to both sides of the equation is \(78\).
To solve the equation \( x - \frac{7}{8} = -5 \), you can add a number to both sides to isolate \( x \).
In this case, you should add \(\frac{7}{8}\) to both sides since it will cancel out the \(-\frac{7}{8}\) on the left side:
\[ x - \frac{7}{8} + \frac{7}{8} = -5 + \frac{7}{8} \]
This simplifies to:
\[ x = -5 + \frac{7}{8} \]
Now, to perform the addition on the right side, convert \(-5\) to a fraction with a denominator of \(8\):
\[ -5 = -\frac{40}{8} \]
Now, add the fractions:
\[ x = -\frac{40}{8} + \frac{7}{8} = -\frac{40 - 7}{8} = -\frac{33}{8} \]
Thus, the number that should be added to both sides of the equation is \(\frac{7}{8}\).
To solve the equation \( x + 0.97 = -2 \), you need to isolate \( x \). You can do this by subtracting \( 0.97 \) from both sides:
\[ x + 0.97 - 0.97 = -2 - 0.97 \]
This simplifies to:
\[ x = -2 - 0.97 \]
Now calculate the right side:
\[ x = -2 - 0.97 = -2.97 \]
Thus, the value of \( x \) is \( -2.97 \).
To solve the equation
\[ x - \frac{9}{4} = -\frac{3}{8}, \]
you need to isolate \( x \). You can do this by adding \(\frac{9}{4}\) to both sides:
\[ x = -\frac{3}{8} + \frac{9}{4}. \]
Next, you need to perform the addition on the right side. To do this, it's helpful to have a common denominator. The common denominator between \(8\) and \(4\) is \(8\).
First, convert \(\frac{9}{4}\) to have a denominator of \(8\):
\[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}. \]
Now substitute back into the equation:
\[ x = -\frac{3}{8} + \frac{18}{8}. \]
Now perform the addition:
\[ x = \frac{18 - 3}{8} = \frac{15}{8}. \]
Thus, the solution of the equation is
\[ x = \frac{15}{8}. \]
