SOLVING FOR A VARIABLE

SIMPLE

Concept: An equation is a mathematical statement that shows that two quantities are equal. When an equation contains a variable, we use algebra to find the value of the variable. To solve an equation means to find the number which replaces the variable to make the mathematical statement true.

The basic strategy in solving an equation with a variable is to isolate the variable, that is, get the variable alone on one side of the equation and the constant terms (numbers) on the other side of the equation. We do this by combining like terms and performing inverse (opposite) operations. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.

Steps To Use When Solving For A Variable

Step 1 | Simplify the equation by combining like terms. If there are like terms on the same side of the equation, simplify the equation by combining the like terms.
Step 2 | If there are like variables on both sides of the equation, eliminate the variable on one side of the equation using addition/subtraction operations.
Step 3 | Whatever is done on one side of the equation in Step 2 must also be done on the other side of the equation now.
Step 4 | Eliminate the non-coefficient numbers from the side of the equation containing the variable by performing inverse operations (opposite operations).
Step 5 | Whatever is done on one side of the equation in Step 4 must also be done on the other side of the equation now.
Step 6 | Eliminate the coefficient of the variable by performing the inverse operation.
Step 7 | Whatever is done on one side of the equation in Step 6 must also be done on the other side of the equation now.
Step 8 | Substitute the solution into the original equation to check the answer.

Example Solve for x: 37x + 40 = 1631.

Step 1 | If there are like terms on the same side of the equation, simplify the equation by combining the like terms. | There are no like terms in this equation to combine.
Step 2 | If there are like variables on both sides of the equation, eliminate the variable on one side of the equation using addition/subtraction operations. | Variables are already limited to one side of this equation.
Step 3 | Whatever is done on one side of the equation in Step 2 must also be done on the other side of the equation now. | Variables are already limited to one side of this equation.
Step 4 | Eliminate the non-coefficient numbers from the side of the equation containing the variable by performing inverse operations (opposite operations). | 37x + 40 = 1631
| The operation is addition. | 37x + 40 = 1631
| The inverse of addition is subtraction. Subtract 40 from 40. | 37x + 40 = 1631 – 40 0
Step 5 | Whatever is done on one side of the equation in Step 4 must also be done on the other side of the equation now. | 37x + 40 = 1631 – 40 0
| Subtract – 40 from 1631. | 37x + 40 = 1631 – 40 – 40 0 1591
| Simplify the equation. | 37x + 40 = 1631 – 40 –40 37x + 0 = 1591 37x = 1591
Step 6 | Eliminate the coefficient of the variable by performing the inverse operation. | 37x = 1591
| The operation is multiplication. | 37x = 1591
| The inverse of multiplication is division. Divide 37x by 37. | 37x = 1591 37
Step 7 | Whatever is done on one side of the equation in Step 6 must also be done on the other side of the equation now. | 37x = 1591 37
| Divide 1591 by 37. | 37x = 1591 37 37
| Simplify the equation. | 37x = 1591 37 37 1x = 43
Step 8 | Substitute the solution into the original equation to check the answer. | 37x + 40 = 1631 37 (43) + 40 = 1631 1591 + 40 = 1631 1631 = 1631