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Chapter 6: Problem 46

Solve and check each equation. \(\frac{3 x}{4}-9=-6\)

Short Answer

Expert verified
The solution to the equation \(\frac{3 x}{4}-9=-6\) is \(x = 4\)

Step by step solution

01

Move the constant term from left side to right side.

Taking the equation \(\frac{3 x}{4}-9=-6\), add 9 to both sides to get rid of -9 on the left. The equation becomes: \(\frac{3 x}{4} = -6+9\)
02

Simplify the right side of the equation.

Adding -6 and 9 gives: \(\frac{3 x}{4} = 3\)
03

Isolate X.

To isolate x, multiply both sides of the equation by \(\frac{4}{3}\). The equation becomes: \(x = 3 * \frac{4}{3}\);
04

Simplify to find x.

Multiplying and simplifying the right side of the equation gives: \(x = 4\);
05

Check the solution.

Substituting \(x = 4\) back into the original equation: \(\frac{3*4}{4}-9\). This simplifies to -6, which is equal to the right side of the original equation, hence the solution is valid;

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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. In an inequality such as \(5 x+4<8 x-5\), I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

Solve the quadratic equations by factoring. \(5 x^{2}+x=18\)

Solve the equations using the quadratic formula. \(x^{2}+4 x=6\)

Solve the equations using the quadratic formula. \(9 x^{2}+6 x+1=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.
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