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Chapter 6: Problem 78

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(2+3(2 x-7)=9-4(3 x+1)\)

Short Answer

Expert verified
The solution to the equation is \(x = 4/3\). In set notation, the solution can be expressed as \(\{4/3\}\).

Step by step solution

01

Distribution

Expand the brackets in equation \(2 + 3(2x - 7) = 9 - 4(3x + 1)\) to get \(2 + 6x -21 = 9 -12x -4\)
02

Simplification

Simplify both sides of the equation to get \(6x - 19 = -12x + 5\)
03

Isolate variable x

Add 12x to both sides to isolate x on one side and numbers on the other side. This gives \(18x - 19 = 5\)
04

Solving for x

Next step is to isolate x by adding 19 to both sides of the equation, which gives \(18x = 24\), then divide both sides of the equation by 18, which gives \(x = 4/3\)

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Most popular questions from this chapter

Solve: \(x^{2}+2 \sqrt{3} x-9=0\).

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+8 x+15\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5\), I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

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