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Chapter 6: Problem 25

Solve and check each equation. \(3 x+5=2 x+13\)

Short Answer

Expert verified
The solution to the equation is \(x = 8\).

Step by step solution

01

Isolate the variable terms

In the given equation \(3x + 5 = 2x + 13\), first move all the terms with \(x\) to one side and the constants to the other. This can be done by subtracting \(2x\) from both sides and 5 from both sides, this leads to the equation \(x = 13 - 5\).
02

Calculate the value

Next, simplify the equation to get the value of \(x\). So, \(x = 8\).
03

Check the solution

Now substitute \(x = 8\) back into the original equation to verify the solution. Substituting \(8\) for \(x\) in the original equation we have \(3(8) + 5 = 2(8) + 13\), which simplifies to \(24 + 5 = 16 + 13\) and further simplifies to \(29 = 29\). Therefore, the solution is correct.

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

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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.

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