Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -7(14b + 11) - 16 = 5 -98b - 77 - 16 = 5 -98b - \square = 5 -98b = 98 b = \square combine like terms divide both sides by -98

Explanation:

Step1: Distribute -7

We start with \(-7(14b + 11)-16 = 5\). Using the distributive property \(a(b + c)=ab+ac\), here \(a = - 7\), \(b=14b\) and \(c = 11\). So \(-7\times14b=-98b\) and \(-7\times11=-77\). So the equation becomes \(-98b-77 - 16=5\).

Step2: Combine constant terms

Now we combine the constant terms \(-77\) and \(-16\). \(-77-16=-93\)? Wait, no, wait the next step in the problem shows \(-98b-\square=5\). Wait, let's recalculate \(-77-16=-93\)? But the problem has \(-98b - \square=5\) and then \(-98b=98\). Wait, maybe I made a mistake. Wait, let's check the problem again. The first step is \(-7(14b + 11)-16=5\). Distribute: \(-98b-77-16 = 5\). Now combine \(-77-16\): \(-77-16=-93\)? But the next line is \(-98b-\square=5\) and then \(-98b = 98\). Wait, maybe there is a typo in my understanding. Wait, if we have \(-98b-77-16=5\), then combining \(-77-16=-93\), so \(-98b-93 = 5\). Then to isolate the term with \(b\), we add 93 to both sides: \(-98b-93 + 93=5 + 93\), so \(-98b=98\). Ah, so the missing term in \(-98b-\square=5\) is 93? Wait, but the problem's next step is \(-98b-\square=5\) and then \(-98b = 98\). So if we have \(-98b - x=5\) and then \(-98b=5 + x\). And then \(-98b = 98\), so \(5 + x=98\), so \(x = 93\). Wait, but let's follow the problem's steps. The problem has:

1. \(-7(14b + 11)-16=5\)
2. \(-98b-77-16=5\)
3. \(-98b-\square=5\) (here we combine -77 and -16: \(-77-16=-93\), so \(\square = 93\))
4. Then we add \(\square\) to both sides: \(-98b-\square+\square=5+\square\), so \(-98b=5 + \square\). Since \(-98b = 98\), then \(5+\square=98\), so \(\square=93\). Then we have \(-98b=98\)
5. Then divide both sides by -98: \(b=\frac{98}{-98}=-1\)

Wait, let's do it step by step as per the problem's structure:

First, distribute: \(-7(14b + 11)-16=5\) gives \(-98b-77-16 = 5\)

Second, combine like terms (the constant terms -77 and -16): \(-77-16=-93\), so the equation becomes \(-98b - 93=5\)

Third, add 93 to both sides: \(-98b-93 + 93=5 + 93\), so \(-98b=98\)

Fourth, divide both sides by -98: \(b=\frac{98}{-98}=-1\)

So the missing term in \(-98b-\square=5\) is 93, then when we add 93 to both sides, we get \(-98b = 98\), and then dividing by -98 gives \(b=-1\)

Step3: Isolate the term with \(b\)

We have \(-98b-93 = 5\). To isolate \(-98b\), we add 93 to both sides of the equation. So \(-98b-93+93 = 5 + 93\), which simplifies to \(-98b=98\)

Step4: Solve for \(b\)

Now we divide both sides of the equation \(-98b = 98\) by -98. So \(b=\frac{98}{-98}=-1\)

Answer:

The missing term in \(-98b-\square=5\) is \(93\), and \(b=-1\)