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Chapter 6: Problem 82

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(5 x-3(x+1)=2(x+3)-5\)

Short Answer

Expert verified
The solution set for the given equation is an empty set, represented in set notation as \(\emptyset\) or \(\{\}\), because the equation has no solutions.

Step by step solution

01

Simplify the left side of the equation

Distribute the multiplication over the brackets: \(5x - 3x - 3 = 2x + 6 - 5\)
02

Simplify both sides of the equation

Combine like terms: \(2x - 3 = 2x + 1\)
03

Rearrange the equation

Subtract \(2x\) from both sides to bring variables on one side: \(-3 = 1\)
04

Analyze the result

The equation \(-3 = 1\) is a false statement. Therefore, this equation has no solutions.

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Most popular questions from this chapter

Solve each equation by the method of your choice. \(x(x+1)=4-(x+2)(x+2)\)

Factor the trinomials in Exercises 9-32, or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+5 x+6\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.

Solve the equations using the quadratic formula. \(x^{2}-5 x=10\)

Solve the quadratic equations by factoring. \(x^{2}+5 x+6=0\)
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