Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Mini Lesson Question

Question #1: Solve Linear Equations

Solve:

2(m - 6) + 3 = m - 1

.

$m = -10$
$m = 14$
$m = 8$
$m = 2$

Solving Linear Equations Using a General Strategy

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation. For example, in $x + 2 = 3$ , the value of the variable $x$ is 1.

To find the solution to an equation in one variable, the goal is to isolate the variable on one side of the equation. For example,

$3 x + 1 = 9 - x$

$+ x + x$

$4 x + 1 = 9$

$- 1 - 1$

$4 x = 8$

You can check the solution by substituting the value into the equation.

$3 (2) + 1 = 9 - 2$

$6 + 1 = 7$

$7 = 7$

Equations may take several steps to solve, so it is helpful to have a clear and organized strategy. The following table shows a general strategy to solve any linear equation in one variable. You may not need to use every step.

General Strategy for Solving Linear Equations

Step 1

Simplify each side of the equation as much as possible.

Use the Distributive Property to remove any parentheses.

Combine like terms .

Step 2

Collect all the variable terms on one side of the equation.

Use the Addition or Subtraction Property of Equality.

Step 3

Collect all the constant terms on the other side of the equation.

Use the Addition or Subtraction Property of Equality.

Step 4

Make the coefficient of the variable term to equal to 1.

State the solution to the equation.

Step 5

Check the solution.

Substitute the solution into the original equation to make sure the result is a true statement.

Try it

Try It: Solving a Linear Equation Using a General Strategy

Solve the following using a general strategy:

Solve $2 (3 x - 8) = 19 - x$ .

Here is how to solve this linear equation, $2 (3 x - 8) = 19 - x$ , using a general strategy:

Distribute.	$2 (3 x - 8) = 19 - x$
Add $x$ to get the variables on the left.	$6 x + x - 16 = 19 - x + x$
Simplify.	$7 x - 16 = 19$
Add 2 to get the constants on the right.	$7 x - 16 + 16 = 19 + 16$
Simplify.	$7 x = 35$
Simplify.	$7 x = 35$
Divide by 7 to make the coefficient of the variable equal to 1.	$\frac{7 x}{7} = \frac{35}{7}$
Simplify.	$x = 5$
Check.	$2 (3 x - 8) = 19 - x$
Substitute 5 for $x$ .	$2 (3 (5) - 8) = 19 - (5)$
Simplify.	$2 (15 - 8) = 14$
Simplify.	$2 (7) = 14$
Simplify.	$14 = 14$ True $✓$

Check Your Understanding

Solve: $7 (n - 3) - 8 = - 15$ .

Multiple Choice:

$n = - \frac{4}{7}$
$n = - 2$
$n = 2$
$n = - 3 \frac{5}{7}$

$n = 2$

Check yourself: After using the Distributive Property and simplifying the left side, the expression is $7 n - 29$ . To isolate the variable, add $29$ to both sides and then divide both sides by $7$ .

Videos: Solving Linear Equations

Khan Academy: Equations with Parentheses

Watch this video to see how to use the Distributive Property to solve an equation with parentheses.

Access multimedia content

Khan Academy: Equations with Variables on Both Sides: Fractions

Watch this video to see how to solve an equation with fractional coefficients and variables on both sides.