To translate and solve the equation, let's break down the given statement step by step.
Step 1: Identify the given statement.
The statement is:
"Eight more than the difference of [tex]\( -5s \)[/tex] and [tex]\( -6s \)[/tex] is equal to the sum of 3 and 7."
Step 2: Translate the words into a mathematical equation.
- The difference of [tex]\( -5s \)[/tex] and [tex]\( -6s \)[/tex] is [tex]\( -5s - (-6s) \)[/tex].
- Eight more than this difference can be written as [tex]\( -5s - (-6s) + 8 \)[/tex].
- The sum of 3 and 7 is written as [tex]\( 3 + 7 \)[/tex].
Combining these, we set up the equation:
[tex]\[ -5s - (-6s) + 8 = 3 + 7 \][/tex]
Step 3: Simplify both sides of the equation.
First, simplify the left side:
[tex]\[ -5s - (-6s) + 8 = -5s + 6s + 8 \][/tex]
This simplifies to:
[tex]\[ (6s - 5s) + 8 = s + 8 \][/tex]
Now, simplify the right side:
[tex]\[ 3 + 7 = 10 \][/tex]
So the equation becomes:
[tex]\[ s + 8 = 10 \][/tex]
Step 4: Solve for [tex]\( s \)[/tex].
Isolate [tex]\( s \)[/tex] by subtracting 8 from both sides of the equation:
[tex]\[ s + 8 - 8 = 10 - 8 \][/tex]
This simplifies to:
[tex]\[ s = 2 \][/tex]
Hence, the solution to the equation is:
[tex]\[ \boxed{s = 2} \][/tex]
