Solving linear equations and inequalities
▶ Same thing to both sides of equations
In this fun math problem, we have a balanced scale with a mystery mass on one side and several 1-kilogram masses on the other. To find the mystery mass, we remove the same number of 1-kilogram masses from both sides, keeping the scale balanced. Then, we can easily determine the mystery mass's weight.
▶ Intro to two-step equations
Here's how we solve a two step equation. It begins with the concept of equality: what we do to one side of the equation must be done to the other.
▶ Two-step equations intuition
This example demonstrates how we solve an equation expressed such: ax + b = c. It's a little more complicated than previous examples, but you can do it!
▶ Worked example: two-step equations
Sal solves the equation -16 = x/4 + 2. It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4.
▶ One-step inequalities examples
Our discussion of linear inequalities begins with multiplying and dividing by negative numbers. Pay attention for the word "swap." Super important!
▶ One-step inequalities: -5c ≤ 15
In addition to solving the inequality, we'll graph the solution. Remember to swap if you mutiply both sides of the inequality by a negative number.
▶ Two-step inequalities
Two-step inequalities are slightly more complicated than one-step inequalities (duh!). This is a worked example of solving ⅔>-4y-8⅓.
▶ Intro to equations with variables on both sides
Learn how to solve the equation 2x + 3 = 5x - 2 with the variable on both sides. We start by visualizing the equation, then isolate the variable by performing the same operations on both sides. Finally, we solve the equation to find the value of the variable.
▶ Equations with variables on both sides: 20-7x=6x-6
Solving equations like 20 - 7x = 6x - 6 with the variable on both sides involves a few steps! First, we add or subtract terms from both sides to separate constants and variables to different sides of the equation. Then, we simplify to isolate the variable. Finally, we check our answer by plugging it back into the original equation.
▶ Equations with parentheses
When an equation such as -9 - (9x - 6) = 3(4x + 6) has parentheses, we can distribute without changing the value of each side. Then combine like terms. Next, we move all the x-terms to one side and the constants to the other. Finally, we solve for x.
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