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Chapter 6: Problem 55

Simplify each algebraic expression. \(5(3 y-2)-(7 y+2)\)

Short Answer

Expert verified
The simplified form of the given expression is \(8y - 12\)

Step by step solution

01

Distribute Multiplication

First distribute the multiplication in the first part of the expression, i.e., \(5(3y - 2)\) which simplifies to \(15y - 10\). The given expression then becomes \(15y - 10 - (7y + 2)\)
02

Apply Sign Change

Next, apply the sign change to the expression inside the brackets to get rid of the brackets. This changes the given expression to \(15y - 10 - 7y - 2\)
03

Combine Like Terms

Finally, combine like terms to simplify the expression. \(15y - 7y = 8y\) and \(-10 - 2 = -12\). So, the final expression is \(8y -12\)

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Most popular questions from this chapter

The formula$$N=\frac{t^{2}-t}{2}$$describes the number of football games, \(N\), that must be played in a league with \(t\) teams if each team is to play every other team once. Use this information to solve. If a league has 45 games scheduled, how many teams belong to the league, assuming that each team plays every other team once?

Explain how to solve a quadratic equation by factoring. Use the equation \(x^{2}+6 x+8=0\) in your explanation.

Solve the equations using the quadratic formula. \(x^{2}+8 x+12=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-x-2\)

Solve the quadratic equations by factoring. \(x^{2}-14 x=-49\)
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