Question

How do you solve 3(x-2)=2(5x+3)

Answer 1

x=−127x equals negative twelve-sevenths\(x=-\frac{12}{7}\)

Explanation:

Simplify the expression\(3(x-2)=2(5x+3)\)

3x−6=10x+63 x minus 6 equals 10 x plus 6\(3x-6=10x+6\)

Add \(6\) to both sides

3x−6+6=10x+6+63 x minus 6 plus 6 equals 10 x plus 6 plus 6\(3x-6+6=10x+6+6\)

3x=10x+123 x equals 10 x plus 12\(3x=10x+12\)

Answer 2

x = -12/7

Explanation:

You want to solve the equation 3(x -2) = 2(5x +3).

Solution

It usually works well to simplify the equation as a first step. Here, that means eliminating parentheses using the distributive property.

3(x -2) = 2(5x +3) . . . . . . . . . . given

3(x) -3(2) = 2(5x) +2(3)

3x -6 = 10x +6 . . . . . . . . . . simplify

Now, we can put the variable terms on one side of the equal sign, and the constant terms on the other side. We do this by subtracting the term we don't want. Each operation is done to both sides of the equation.

-6 = 7x +6 . . . . . . . . . subtract 3x from both sides

-12 = 7x . . . . . . . . . subtract 6 from both sides

x = -12/7 . . . . . . . divide by the coefficient of x

The value of x is -12/7.

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Additional comment

The attached calculator display shows this value of x makes both sides of the equation equal, which confirms this solution. We choose to check our solution this way so we don't have to do the arithmetic with fractions by hand.

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