Matching Equations To Problems

Solve Equations

Formative Assessment

Summary of the Math: Solve Equations

Read and Discuss

Follow the steps and justifications below.

  • Identify variables in the starting equation:

y − 2x − 7 = x + 3

  • Add 2x + 7 to both sides by the addition property of equality:

(y −2x − 7) + (2x + 7) = (x + 3) + (2x + 7)

  • Rearrange terms using properties of operations:

y + (2x − 2x) + (7 − 7) = (x + 2x) + (3 + 7)

  • Combine like terms using the distributive property:

y + x(2 − 2) + 0 = x(1 + 2) + 10

  • Simplify both sides to get a new equation:

y = 3x + 10

In this example, 2x + 7 is added to both sides of the equation. But any number could have been added, and the resulting equation would still have been true, as long as the same number was added to both sides. Notice how parentheses are used to keep terms organized, and how the associative property and commutative property of addition are used to rearrange the terms.

Hint:

Can you explain how to use properties of operations to solve equations?