Could you give me an example of a linear equation with a variable on both sides of the equal sign? Please don't look one up. You don't have to give the answer to the equation. It can only have one solution.
5x = 2x + 15
Sure! Here's an example of a linear equation with a variable on both sides of the equal sign:
3x + 2 = 5x - 1
In this equation, the variable "x" is on both sides of the equal sign.
Sure! To come up with a linear equation that has a variable on both sides of the equal sign, we can start by selecting a value for the variable and then create an equation based on that value. Let's choose the value 2 for the variable.
First, we start with the general form of a linear equation which is:
ax + b = cx + d
Let's say a = 3 and c = 5, and we'll assign b and d as constants. Now, we can create the equation:
3x + b = 5x + d
To ensure that the equation has only one solution, we need to guarantee that the coefficients of x on both sides are different. In this case, 3 and 5 are different coefficients, so we have met that requirement.
To complete the equation, we can substitute the chosen value of 2 for x and select random values for b and d. For example, let's say b = 7 and d = 9. The equation would then be:
3(2) + 7 = 5(2) + 9
6 + 7 = 10 + 9
13 = 19
In this case, the equation is not true since 13 is not equal to 19. However, this is an example of a linear equation with a variable on both sides of the equal sign.