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Chapter 6: Problem 37

Solve and check each equation. \(3(x+1)=7(x-2)-3\)

Short Answer

Expert verified
The solution to the equation is \(x = 5\).

Step by step solution

01

Simplify the equation

Distribute the numbers outside the brackets on both sides. On the left side, 3 is distributed to both \(x\) and 1. On the right side, 7 is distributed to \(x\) and -2. The equation now becomes \(3x+3=7x-14-3\)
02

Consolidate like terms

On the right side of the equation, combine -14 and -3. The equation now becomes \(3x+3=7x-17\)
03

Move the variable term to one side

Subtract \(7x\) from both sides of the equation, moving the \(x\) term to one side. The equation now becomes \(-4x+3=-17\)
04

Move the constant to the other side

Subtract 3 from both sides of the equation, moving the constant number to the right side. The equation now becomes \(-4x=-20\)
05

Solve for the variable x

Divide both sides of the equation by -4. This isolates \(x\) on one side. The solution is \(x = 5\)
06

Verify the solution

Substitute \(x = 5\) into the original equation, \(3(x+1)=7(x-2)-3\). If both sides of the equation equal each other, then the answer is verified. Indeed, substituting \(x = 5\) into the equation, we get \(3(5+1)=7(5-2)-3\), which simplifies to 18=18, verifying the solution.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. It's easy to factor \(x^{2}+x+1\) because of the relatively small numbers for the constant term and the coefficient of \(x\).

Solve the equations using the quadratic formula. \(x^{2}+2 x=4\)

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

Solve the quadratic equations by factoring. \(x^{2}-4 x=21\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-x-90\)
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