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Chapter 6: Problem 24

Solve and check each equation. \(11 x-(6 x-5)=40\)

Short Answer

Expert verified
The solution to the equation \(11 x-(6 x-5)=40\) is \(x = 7\)

Step by step solution

01

Simplify the equation

First, distribute the subtraction across the parentheses on the left side of the equation: \(11x - 6x + 5 = 40\)
02

Combine like terms

Combine the \(x\) terms on the left side, which results in: \(5x + 5 = 40\)
03

Solve for \(x\)

Subtract 5 from both sides of the equation to isolate \(5x\), giving \(5x = 35\). Then, divide both sides by 5 to solve for \(x\): \(x = 7\) .
04

Check the solution

Substitute \(x = 7\) into the original equation: \(11(7)-(6(7)-5)\). Simplifying it gives 77 - 42 which equals 35, confirming the solution is correct.

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Most popular questions from this chapter

The formula$$N=\frac{t^{2}-t}{2}$$describes the number of football games, \(N\), that must be played in a league with \(t\) teams if each team is to play every other team once. Use this information to solve Exercises 83-84. If a league has 36 games scheduled, how many teams belong to the league, assuming that each team plays every other team once?

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

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

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Solve the equations using the quadratic formula. \(6 x^{2}-5 x-6=0\)
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