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Chapter 6: Problem 62

Simplify each algebraic expression. \(7 x-4[6-(8-5 x)]\)

Short Answer

Expert verified
The simplified form of the algebraic expression \(7 x-4[6-(8-5 x)]\) is \(27x + 8\).

Step by step solution

01

Distribute the Negative Sign Inside the Bracket

The first step is to distribute the negative sign into the elements inside the bracket. It is important to remember that when a negative sign is distributed, it changes the sign of the terms inside the bracket. Thus, \(7x - 4[6 - (8 - 5x)]\) becomes \(7x - 4[6 - 8 + 5x]\).
02

Further Simplify the Inside Bracket

Next, further simplify by combining like terms inside the bracket, which results in \(7x - 4[-2 + 5x]\).
03

Distribute 4 Inside the Bracket

Distribute 4 inside the bracket to every term to get \(7x - 4 * -2 + 4 * 5x\), which simplifies to \(7x + 8 + 20x\).
04

Combine Like Terms

Finally, combine the like terms to get the simplified expression. \(7x + 20x + 8\) becomes \(27x + 8\).

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(x^{2}+2 x=4\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-8 x+32\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(8 x^{2}+33 x+4\)

Use FOIL to find the products. \((x-5)(x+3)\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)
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