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Chapter 6: Problem 40

Solve and check each equation. \(7(3 x-2)+5=6(2 x-1)+24\)

Short Answer

Expert verified
The solution to the equation is \(x = 3\).

Step by step solution

01

Simplify the Equation

To simplify an equation, distribute the numbers outside the brackets with the numbers inside the brackets on both sides of the equation. The equation then becomes: \(21x - 14 + 5 = 12x - 6 + 24\). Simplifying further gives: \(21x - 9 = 12x + 18\)
02

Solving for the Variable

In order to isolate the variable, subtract \(12x\) from both sides of the equation, the equation will then become: \(9x - 9 = 18\). Then, add 9 to both sides of the equation to get: \(9x = 27\). Dividing through by 9, we find that \(x = 3\)
03

Checking the Solution

Substitute the value of \(x = 3\) back into the original equation: \(7(3(3)-2)+5 = 6(2(3)-1)+24\). This simplifies to: \(58 = 58\). Since both sides of the equation are equal, the solution is correct.

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Most popular questions from this chapter

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

Solve the quadratic equations by factoring. \(x^{2}+7 x=18\)

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

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

Explain how to factor \(x^{2}-5 x+6\).
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