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Problem 186

Solve the equation $$4 x-5=x+7$$

Expert verified
The solution to the equation $$4x - 5 = x + 7$$ is $$x = 4$$.
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Step 1: Move all terms with x to one side of the equation

Subtract $$x$$ from both sides of the equation to collect the $$x$$ terms on one side. This will give us: $4x - 5 - x = x + 7 - x$ $3x - 5 = 7$

Step 2: Move all constant terms to the other side of the equation

To isolate x, we need to move the constant term (-5) to the other side of the equation. We do this by adding 5 to both sides: $3x - 5 + 5 = 7 + 5$ $3x = 12$

Step 3: Divide both sides of the equation by the coefficient of x

Now, we need to find the value of x by dividing both sides of the equation by the coefficient of x (which is 3): $\frac{3x}{3} = \frac{12}{3}$ $x = 4$ So, the solution to the equation $$4x - 5 = x + 7$$ is $$x = 4$$.

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