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Chapter 6: Problem 45

Solve and check each equation. \(\frac{2 x}{3}-5=7\)

Short Answer

Expert verified
The solution to the equation \(\frac{2x}{3}-5=7\) is \(x=18\)

Step by step solution

01

Add 5 to Both Sides

The first logical step is to get rid of the 5 on the left side of the equation by adding 5 on both sides. This will isolate the x term on the left side. The equation becomes: \(\frac{2x}{3} - 5 + 5 = 7 + 5\) which simplifies to \(\frac{2x}{3} = 12\)
02

Multiply Both Sides by 3

The next step is to isolate the fraction by multiplying both sides by 3. This will give us: \(2x = 36\)
03

Divide by 2

Finally, to isolate x, we should divide both sides by 2. This yields: \(x = 18\)
04

Verify the Solution

To ensure the solution is correct, we should substitute x=18 in the original equation. This gives us: \(\frac{2*18}{3}-5=7\), which simplifies to: 12-5=7. So, the solution x=18 is accurate.

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