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Chapter 6: Problem 81

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(4(x+2)+1=7 x-3(x-2)\)

Short Answer

Expert verified
The solution set for the equation is \( \emptyset \) since there is no real number when substituted for x will make the equation valid.

Step by step solution

01

Distribute

Distribute the numbers before brackets: \(4x+8+1=7x-3x+6\). Simpify to get \(4x+9=4x+6\).
02

Start Isolating

Start isolating x by subtracting \(4x\) from each side to get \(9=6\).
03

Identify and Express the Solution

In this stage, look at the result. Since \(9\) is not equal to \(6\), the initial equation given has no solution. To express this fact differently, using the set notation, you state that the solution set for the equation is the empty set, denoted \( \emptyset \). In other words, there are no real numbers you can substitute for x that will make the equation true.

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(x^{2}-3 x=18\)

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