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Chapter 6: Problem 91

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

Short Answer

Expert verified
The solution to the equation is \(x=0\).

Step by step solution

01

Simplify the Left Side of Equation

Combine like terms on the left side of the equation. To do this, obtain a common denominator for \(\frac{x}{2}\) and \(\frac{x}{4}\). Common denominator is 4, multiply \(\frac{x}{2}\) by 2 to obtain equivalent fraction with 4 as denominator. \(\frac{2x}{4}-\frac{x}{4}+4 = x+4\). Simplified it becomes \(\frac{x}{4}+4=x+4\).
02

Simplify the Equation

Subtract 4 from both sides to get rid of the +4 on both sides. The new equation will be \(\frac{x}{4}=x\).
03

Clear Fraction

Multiply by 4 on both sides of the equation to clear the fraction on left side. We get \(x=4x\).
04

Simplify the Equation

Subtract x from both sides of the equation to isolate x. This yields \(0=3x\).
05

Solve for x

Divide both sides of the equation by 3 to solve for x. We find that \(x=0\).

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-4 x-5\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The fastest way for me to solve \(x^{2}-x-2=0\) is to use the quadratic formula.

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

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-7 x-44\)

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.
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