twice the difference of a number and 3 is equal to 3 times the sum of a number and 2

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twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.

We've got 2 algebraic expressions here. Let's take them in parts.

Left side algebraic expression: twice the difference of a number and 3

• The phrase a number means an arbitrary variable, let's call it x.
• The word difference means we subtract 3 from the variable x
• x - 3
• Twice this difference means we multiply (x - 3) by 2
• 2(x - 3)

Right side algebraic expression: 3 times the sum of a number and 2

• The phrase a number means an arbitrary variable, let's call it x.
• The word sum means we add 2 to the variable x
• x + 2
• 3 times the sum means we multiply (x + 2) by 3
• 3(x + 2)

Now, we have both algebraic expressions, the problem says is equal to
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
2(x - 3) = 3(x + 2)