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Chapter 6: Problem 22

Solve and check each equation. \(10(3 x+2)=70\)

Short Answer

Expert verified
The solution to the equation \(10(3x+2)=70\) is \(x=5/3\).

Step by step solution

01

Simplify the equation

Distribute 10 through the expression within the brackets: \(10(3x) + 10(2) = 70\), which simplifies to \(30x + 20 = 70\).
02

Isolate the variable

Subtract 20 from both sides of the equation to isolate \(30x\) and obtain \(30x=50\).
03

Solve for the variable

Divide both sides of the equation by 30 to find the value of \(x\). So \(x = 50/30 = 5/3\).
04

Check the solution

Substitute \(x = 5/3\) back into the original equation \(10(3 x+2)=70\). Simplification gives \(10(3 * (5/3) +2) = 70\), which simplifies to \(70=70\). Both sides of the equation are equal, therefore, the solution is correct.

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x+81\)

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.

In Exercises 73-80, solve each equation by the method of your choice. \(\frac{3 x^{2}}{4}-\frac{5 x}{2}-2=0\)

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Solve the equations using the quadratic formula. \(x^{2}-5 x=10\)
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