Certainly! Let's solve the given equation step-by-step:
The given equation is:
[tex]\[ 42 \div (\quad) = -7 \][/tex]
We need to find the value that, when 42 is divided by it, results in -7.
Step 1: Let's introduce a variable to represent the unknown value. Let [tex]\(x\)[/tex] be that unknown value.
So, our equation becomes:
[tex]\[ 42 \div x = -7 \][/tex]
Step 2: Rewrite the division as a multiplication problem. Recall that dividing by a number is the same as multiplying by its reciprocal. Therefore, our equation becomes:
[tex]\[ \frac{42}{x} = -7 \][/tex]
Step 3: To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation. We can do this by multiplying both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[ 42 = -7x \][/tex]
Step 4: Now, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(-7\)[/tex]:
[tex]\[ x = \frac{42}{-7} \][/tex]
Step 5: Perform the division:
[tex]\[ x = -6 \][/tex]
So, the correct value for [tex]\(x\)[/tex] is:
[tex]\[ x = -6 \][/tex]
Therefore, the solution to the equation [tex]\(42 \div (\quad) = -7\)[/tex] is [tex]\(-6\)[/tex].
