/*! 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 100 Solve: \(2(x-9)=5 x-3(x+7)\)... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 100

Solve: \(2(x-9)=5 x-3(x+7)\)

Short Answer

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Step by step solution

01

Distribute Terms

Expand both sides of the equation. On the left side, distribute the 2: \[ 2(x - 9) = 2x - 18 \] On the right side, distribute the -3: \[ 5x - 3(x + 7) = 5x - 3x - 21 \]
02

Simplify Both Sides

Combine like terms on the right side of the equation. \[ 5x - 3x - 21 = 2x - 21 \] Now the equation looks like: \[ 2x - 18 = 2x - 21 \]
03

Isolate the Variable

Subtract \(2x\) from both sides to isolate the variable: \[ 2x - 18 - 2x = 2x - 21 - 2x \] The equation simplifies to: \[ -18 = -21 \]
04

Evaluate the Truth of the Equation

Since the simplified equation \(-18 = -21\) is false, there is no solution. Thus, the original equation has no values of \(x\) that satisfy it.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The distributive property helps us expand expressions. When you see something like 2(x - 9), you need to distribute the 2 to both terms inside the parentheses. This means multiply 2 by every term inside the parentheses: o2(x - 9) = 2 * x + 2 * (-9)oThis simplifies to: 2x - 18On the right side of the equation, we have 5x - 3(x + 7). Again, distribute the -3 through the parentheses:o-3(x + 7) = -3 * x + (-3) * 7oThis simplifies to: -3x - 21Now you combine it with the 5x: 5x - 3x - 21
Combining Like Terms
Combining like terms is a crucial step to simplify equations. Like terms are terms that contain the same variables to the same power. In our equation, on the right side, we have: o5x - 3x - 21You can combine the x terms: o5x - 3x = 2xSo now, the equation looks like this: 2x - 18 = 2x - 21
Isolating the Variable
Isolating the variable involves getting the variable by itself on one side of the equation. In our case, we have: 2x - 18 = 2x - 21To isolate x, we need to subtract 2x from both sides:o2x - 18 - 2x = 2x - 21 - 2xThis simplifies to:o-18 = -21
No Solution in Algebra
Sometimes, when you solve an equation, you may come across a statement that is false. This means there is no solution. In our problem:o-18 = -21This statement is not true, meaning no value of x can satisfy this equation. Thus, the equation has no solution.

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Most popular questions from this chapter

Use the slope formula to find the slope of the line that passes through the points. \((0,-9) ;(-2,0)\)

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