Unit 7 lesson 4 solve equations with multiplication and division
To solve equations involving multiplication and division, follow these steps:
1. Simplify the equation by combining like terms on both sides, if necessary.
2. Isolate the variable by undoing the multiplication or division operations.
a) If the variable is multiplied by a number, divide both sides of the equation by that number.
b) If the variable is divided by a number, multiply both sides of the equation by that number.
3. Solve for the variable by performing the necessary operation(s) on both sides of the equation.
4. Check your solution by substituting it back into the original equation and simplifying both sides of the equation to ensure they are equal.
Example 1: Solve the equation 6x = 48
1. The equation is already simplified.
2. To isolate the variable, divide both sides of the equation by 6:
6x/6 = 48/6
x = 8
3. The solution is x = 8.
4. Checking the solution: Substitute x = 8 back into the original equation:
6(8) = 48
48 = 48 (Both sides are equal, so the solution is correct.)
Example 2: Solve the equation 3y/4 = 6
1. The equation is already simplified.
2. To isolate the variable, multiply both sides of the equation by 4/3:
(3y/4) * (4/3) = 6 * (4/3)
y = 8
3. The solution is y = 8.
4. Checking the solution: Substitute y = 8 back into the original equation:
(3(8))/4 = 6
24/4 = 6
6 = 6 (Both sides are equal, so the solution is correct.)
Remember to always check your solution, as it helps ensure the accuracy of your work.