To set up an equation based on the statement given, first identify the unknown number, and we can call it "x". The statement says "five times a number plus four" which translates to 5x + 4. It also states this equals "three times that same number plus ten", which is 3x + 10.
Now we set up the equation that equates these two expressions:
5x + 4 = 3x + 10
This equation represents the situation described in the statement. Now, let's solve it step-by-step:
1. Subtract 3x from both sides to get the terms with x on one side:
5x + 4 - 3x = 3x + 10 - 3x
2. This simplifies to:
2x + 4 = 10
3. Now subtract 4 from both sides to isolate the terms with x:
2x + 4 - 4 = 10 - 4
4. This simplifies to:
2x = 6
5. Finally, divide both sides by 2 to solve for x:
2x / 2 = 6 / 2
x = 3
So, the number we are looking for is 3.
