Equations and algebraic relationships — study worksheet

1. Read the core idea

An equation states that two expressions are equal. Preserve equality by applying the same operation to both sides. Combine like terms before isolating the unknown, and use the distributive property when parentheses occur. Substitute the solution into the original equation to catch arithmetic or sign errors. An inequality follows similar steps, but multiplying or dividing by a negative reverses its direction.

2. Trace the worked example

For 2(x + 3) = 18, divide by 2 to obtain x + 3 = 9, then subtract 3: x = 6. Substitution gives 2(9) = 18.

Write the steps or relationships that explain the result:

3. Use the method

Simplify, undo addition or subtraction, undo multiplication or division, then substitute.

Summarize the method in your own words, with a diagram or labeled units where useful:

4. Record a mistake to avoid

Do not distribute to only one term inside parentheses.

Describe how you will recognize and correct this mistake:

5. Review after practice

Use the mixed practice check linked in the hub. Record the skill you need to revisit and your next study step.