Question

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ora ii classes (9th grade - 11th grade)
rough december 19th. you may assign this assessment anytime in the window.
what value of x satisfies the equation
$-3(4x - 5) = 2(1 - 5x)$?

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side: \(-3(4x - 5)=-3\times4x+(-3)\times(-5)=-12x + 15\).
We expand the right - hand side: \(2(1 - 5x)=2\times1-2\times5x = 2-10x\).
So the equation becomes \(-12x + 15=2-10x\).

Step2: Move like terms together

Add \(12x\) to both sides of the equation to get all the \(x\) terms on one side: \(-12x+12x + 15=2-10x + 12x\).
Simplifying, we have \(15=2 + 2x\).
Then subtract 2 from both sides: \(15-2=2-2 + 2x\).
Simplifying, we get \(13 = 2x\).

Step3: Solve for x

Divide both sides of the equation \(13 = 2x\) by 2: \(x=\frac{13}{2}=6.5\).

Answer:

\(x = \frac{13}{2}\) (or \(x = 6.5\))