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Chapter 6: Problem 41

Solve and check each equation. \(6=-4(1-x)+3(x+1)\)

Short Answer

Expert verified
The solution to the equation is \(x=\frac{5}{7}\).

Step by step solution

01

Distribute Multiplication Inside Parentheses

Start by applying the distributive property to eliminate parentheses in the equation, which transforms the equation into: \(6=-4+4x+3x+3\).
02

Combine Like Terms

Combine similar terms on the right side of the equation: \(4x+3x=-4+3+6\); this gives \(7x=5\).
03

Isolate the Variable 'x'

Now, isolate the variable 'x' by dividing every term by 7: \(x=\frac{5}{7}\).
04

Check the Solution

To ensure correctness of the solution, substitute \(\frac{5}{7}\) back into the original equation: \(6=-4(1-\frac{5}{7})+3(\frac{5}{7}+1)\). This simplifies to \(6=6\), confirming that the solution is correct.

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Most popular questions from this chapter

Solve the quadratic equations by factoring. \(x(6 x+23)+7=0\)

Solve each equation using the zero-product principle. \((4 x+5)(x-2)=0\)

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

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

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