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Chapter 6: Problem 59

Simplify each algebraic expression. \(7-4[3-(4 y-5)]\)

Short Answer

Expert verified
The simplified form of the algebraic expression \(7-4[3-(4 y-5)]\) is \(-25 + 16y\).

Step by step solution

01

Simplify the Inner Parentheses

The first step is to subtract 4y from 5, which is inside the innermost parentheses. This results in \(7 - 4[3-(4y-5)] = 7 - 4[3-4y+5]\)
02

Simplify Inside the Brackets

Next, the operation inside the brackets are performed by adding 3 and 5, which results in 8. Hence, \(7 - 4[3-4y+5] = 7 - 4[8-4y]\)
03

Distribute the multiplication inside the brackets

Now, distribute the negative 4 inside the brackets by multiplying -4 with each of the terms inside the brackets which results in \(7 - 4[8-4y] = 7 - 4*8 + 4*4y = 7 - 32 + 16y \)
04

Perform the Addition and Subtraction

Finally, perform the subtraction and addition operation to get the simplified expression. Thus, \(7 - 32 + 16y = -25 + 16y\)

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Most popular questions from this chapter

In Exercises 73-80, solve each equation by the method of your choice. \(\frac{3 x^{2}}{4}-\frac{5 x}{2}-2=0\)

Solve the equations using the quadratic formula. \(x^{2}+5 x+3=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-14 x+45\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(2 x^{2}+5 x-3\)
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