# 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(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

 Algebra Main Page Positive & Negative Numbers Addition & Subtraction of Positive & Negative Numbers Multiplication of Positive & Negative Numbers Division of Positive & Negative Numbers Order of Operations Exponents Scientific Notation Equations 1 Equations 2 Equations 3 Equations 4 Equations 5 Equations 6 Equations 7 Equations 8 Equations 9