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Chapter 6: Problem 61

Simplify each algebraic expression. \(8 x-3[5-(7-6 x)]\)

Short Answer

Expert verified
The simplified expression of \(8x - 3[5 - (7-6x)]\) is \(-10x + 6\).

Step by step solution

01

Simplify the expression within the innermost brackets

Begin by working on the expression within the most inner brackets, \(7-6x\). In this case, there's nothing to simplify, so the expression remains as is.
02

Substitute the result in the larger expression

The next step is to substitute the result from Step 1 into the larger expression. Therefore, \( 8x - 3[5 - (7-6x)] \) will be simplified to \(8x - 3 * (5 - (7-6x)) \). Now, calculate the value of the expression within the outer brackets. This is done by subtracting the value \(7 - 6x\) from 5.
03

Distribute

Simplify the expression above by distributing the terms inside the brackets. This leads to \(8x - 3*(5 - 7 + 6x) \) and further simplifying gives \( 8x - 3*(-2 + 6x) \). This can be further simplified by distributing the -3 in the brackets to give \( 8x + 6 - 18x \).
04

Combine like terms

The last step in simplifying an algebraic expression is combining like terms. This gives \( -10x + 6 \) as the simplified algebraic expression.

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-2 x-15\)

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

Solve each equation using the zero-product principle. \((4 x+5)(x-2)=0\)

In Exercises 98-99, find all positive integers b so that the trinomial can be factored. \(x^{2}+b x+15\)

Use FOIL to find the products. \((2 x-1)(x+2)\)
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