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Solving equations & inequalities: FAQ

Frequently asked questions about solving equations & inequalities

Why do we need to learn about linear equations?

Linear equations are a fundamental part of algebra, and they're often used to model real-world situations. For example, someone might use a linear equation to figure out how much money they will have left after spending a certain amount each week, or to calculate the distance they travel on a road trip when they know their average speed and time.

What does it mean to have variables on "both sides" of an equation?

This refers to a linear equation where we have a letter on both sides of the equals sign. For example, 3x+4=2x+7 has variables on both sides, but 3x+4=10 does not.

What's the difference between a multi-step inequality and a compound inequality?

A multi-step inequality has more than one operation in it, for example 2x5>7. A compound inequality is the combination of two inequalities, for example x>3 AND x<7.

How do we figure out the number of solutions to a linear equation?

One way to figure out how many solutions there are to a linear equation is to try to isolate the variable on one side of the equation.
  • For an equation with one solution, consider the equation 2x+3=11. If we isolate the variable, we find that x=4.
  • For an equation with no solution, consider the equation 2x+3=2x+7. If we try to isolate the variable, we end up with a false statement like 3=7 when we subtract 2x from both sides of the equation. Since 3 does not equal 7, there is no solution to this equation.
  • For an equation with infinite solutions, consider the equation 2x+3=2x+3. If we try to isolate the variable, we end up with a statement that is always true like 3=3 when we subtract 2x from both sides of the equation. Since 0 = 0 is always true, any value of x will satisfy the original equation. So there are infinite solutions.

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