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Chapter 6: Problem 19

Solve and check each equation. \(14-5 x=-41\)

Short Answer

Expert verified
The solution is \(x = 11\).

Step by step solution

01

Simplifying expression

To isolate \(x\), start by isolating the term involving \(x\) on one side of the equation. We do this by moving all the other terms to the other side of equation. The equation then becomes: \(5x = 14 + 41\).
02

Calculating the right-hand side

By adding 14 and 41 on the right-hand side we get: \(5x = 55\).
03

Solving for \(x\)

To get the variable \(x\), we divide the equation by the coefficient of \(x\), which is 5. Thus we get: \(x = \frac{55}{5} = 11\).
04

Checking the solution

To validate our solution, we substitute \(x = 11\) back into the original equation and check if the left-hand side equals the right-hand side. So: \(14 - 5 \times 11 = -41\), which is the correct value therefore our solution is correct.

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Most popular questions from this chapter

Solve each equation using the zero-product principle. \((x+9)(3 x-1)=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)

The radicand of the quadratic formula, \(b^{2}-4 a c\), can be used to determine whether \(a x^{2}+b x+c=0\) has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation? Explain.

In Exercises 98-99, find all positive integers b so that the trinomial can be factored. \(x^{2}+b x+15\)

Solve the equations using the quadratic formula. \(x^{2}-x=14\)
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