Questions: Simplify the following expression. -3+7(a-3b-1)-4(10-a+2b)

Simplify the following expression. -3+7(a-3b-1)-4(10-a+2b)
Transcript text: Simplify the following expression. \[ -3+7(a-3 b-1)-4(10-a+2 b) \]
failed

Solution

failed
failed

Solution Steps

To simplify the given expression, we need to distribute the constants across the terms inside the parentheses and then combine like terms. This involves applying the distributive property and then simplifying the resulting expression by combining terms with the same variables.

Step 1: Distribute Constants Across Parentheses

To simplify the expression \(-3 + 7(a - 3b - 1) - 4(10 - a + 2b)\), we first distribute the constants \(7\) and \(-4\) across the terms inside the parentheses:

\[ 7(a - 3b - 1) = 7a - 21b - 7 \]

\[ -4(10 - a + 2b) = -40 + 4a - 8b \]

Step 2: Combine Like Terms

Next, we combine all the terms from the expanded expression:

\[ -3 + 7a - 21b - 7 - 40 + 4a - 8b \]

Combine the like terms:

  • Constant terms: \(-3 - 7 - 40 = -50\)
  • Terms with \(a\): \(7a + 4a = 11a\)
  • Terms with \(b\): \(-21b - 8b = -29b\)
Step 3: Write the Simplified Expression

The simplified expression is:

\[ 11a - 29b - 50 \]

Final Answer

The expression simplifies to:

\[ \boxed{11a - 29b - 50} \]

The correct answer from the given options is the first one: \(11a - 29b - 50\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The growth of the number of students taking at least one online course can be approximated by a logistic function with k=0.0463, where t is the number of years since 2002. In 2002 (when t=0), the number of students enrolled was 1.659 million. Assume that the number will level out at around 7.3 million students. (a) Find the growth function G(t) for the number of students (in millions) enrolled in at least one online course. Find the number of students enrolled in at least one online course and the rate of growth in the number for the following years. (b) 2003 (c) 2010 (o) What happens to the rate of growth over time? (d) 2017
failedAnswered
The graph is shown for f(x) = (x^4 + 3x^3 - 39x^2 - 47x + 210) / (x^4 - 2x^3 - 21x^2 + 22x + 40) This function can be expressed in factored form as: f(x) = (x+3) * (x-5) * (x+7) * (x-2) / (x+4) * (x-5) * (x+1) * (x-2) Which of the following is a TRUE statement? There are discontinuities at x=-4, x=-1, x=2, and x=5, which cause the denominator to become zero. There are discontinuities at x=-4 and x=-1 only (nowhere else), which are shown as locations of vertical asymptotes. There are discontinuities at x=2 and x=5 only (nowhere else), which are shown as holes in the graph.
failedAnswered
True or false: Reporting comprehensive income can be done with a single, continuous statement or in two separate, but consecutive statements.
failedAnswered
Currently in Economica, the frictional rate of unemployment is 1.0%, the structural rate of unemployment is 1.5%, and the cyclical rate of unemployment is 3.0%. In the winter, there is seasonal unemployment of 1%. In this country, the seasonally adjusted natural rate of unemployment would be considered to be %. (Round your response to one decimal place.)
failedAnswered
The nurse is caring for a patient with seizures who was prescribed phenytoin IV. The primary health care provider has replaced this drug with fosphenytoin. Which would be the most likely reason for replacing phenytoin? Select all that apply. One, some, or all responses may be correct. Fosphenytoin is suitable with glucose solutions. Fosphenytoin has reduced allergic manifestations. Fosphenytoin can be administered at a higher push rate. Fosphenytoin can be given via the intramuscular route.