Given the statement:
Three times a number, decreased by 4, is the same as double the difference of the number and 1.
Let's translate the statement to an equation and solve.
Let x represent the unknown number.
We have:
• Three times a number decreased by 4: ,3x - 4
• Double the difference of the number and 1: ,2(x - 1)
Since both expressions are the same, let's equate the expressions:
3x - 4 = 2(x - 1)
Let's solve for x.
• Apply distributive property to the right side of the equation:
3x - 4 = 2x - 2(1)
3x - 4 = 2x - 2
• Add 4 to both sides of the equation:
3x - 4 + 4 = 2x - 2 + 4
3x = 2x + 2
• Subtract 2x from both sides of the equation:
3x - 2x = 2x - 2x + 2
x = 2
Therefore, we have the solution:
x = 2
• ANSWERS:
Equation: 3x - 4 = 2(x - 1)
Solution: x = 2