EQUATIONS
9
Simplifying Expressions
in Equations
After doing this page, try the Equations
9 Quiz.
RECAP: We have been introduced to
variables in equations. Now let's look at simplifying some equations with addition
and subtraction.
Here is a simple one to start. In
this equation we must simplify the equation to find the value of the variable.
The equation is two times x plus four plus three times x plus five equals forty-eight.
- First, multiply the two times
the x and two times the four in parenthesis.
- Then multiply the three times
the x and the five in parenthesis.
- Then add the two x and the three
x together to get five x and add the eight and fifteen to get twenty-three.
- Next solve five x plus twenty-three
equals forty eight. Subtract or take twenty-three from both sides of the equation.
The equation then states five x equals twenty-five. Divide each side by five
and the variable x equals 5.
- By putting the five into the equation
we see that it works. Two times five plus four plus three times five plus
five equals forty-eight.
2(x + 4) + 3(x +
5) = 48
2x + 8 + 3x + 15 =48
5x + 23 =48
5x = 25
2(5 + 4) + 3(5 +
5) = 48
2(9) + 3(10) = 48
18 + 30 = 48
Here is another example, four times
x minus seven minus three times x plus five equals two times x plus five plus
three times x minus ten.
4(x - 6) -3(x + 5)
= 2(x + 3) + 2(x - 6)
4x - 24 - 3x - 15 = 2x + 6 + 2x - 12
x - 39 = 4x - 6
-33 = 3x
-11 = x
4(-11-6) -3(-11 +5) = 2(-11 +3) + 2(-11 -6)
4(-17) -3(-6) = 2(-8) + 2(-17)
-68 +18 = -16 -34
-50=-50
