/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 126 Solve each equation. $$\begin{... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 126

Solve each equation. $$\begin{aligned} 45-[4-2 x-4(x+7)] &=\\\ -4(1+3 x)-[4-3(x+2)-2(2 x-5)] \end{aligned}$$

Short Answer

Expert verified
The solution for equation 1 is \(x=-11.5\) and for equation 2 is \(x= 2.4\)

Step by step solution

01

Simplify the expression within innermost parentheses

For Equation 1: \[45-[4-2 x-4(x+7)]\]\n This simplifies to: \[45-[4-2x-4x-28]\] which further simplifies to: \[45-[4-6x-28]\]For Equation 2: \[-4(1+3 x)-[4-3(x+2)-2(2 x-5)]\]This simplifies to: \[-4(1+3x)-[4-3x-6-2(2x-5)]\] which further simplifies to: \[-4(1+3x)-[4-3x-6-4x+10]\]
02

Continue simplifying the equations

For Equation 1: \[45-[4-6x-28]\] further simplifies to: \[45-[-6x-24]\]For Equation 2: \[-4(1+3x)-[4-3x-6-4x+10]\] further simplifies to: \[-4(1+3x)-[-7x+8]\]
03

Final simplification and solving for \(x\)

Equation 1 simplifies to: \[45+6x+24 = 0\] Solving for \(x\): \[6x=-69, x =-11.5\]Equation 2 simplifies to: \[-4-12x+7x-8=0\] Solving for \(x\): \[-5x=-12, x = 2.4\]

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Most popular questions from this chapter

$$\text { Solve for } t: \quad s=-16 t^{2}+v_{0} t$$

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

How is the quadratic formula derived?

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

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