Solve two-step equations · lesson

Undo in reverse order

💡 Undo adding or subtracting first, then undo multiplying or dividing.

In 4x + 9, x was multiplied by 4, then 9 was added. To undo, go backward.

First subtract 9 from both sides. Then divide both sides by 4.

If x has a negative coefficient, divide by the negative number. Check your answer at the end.

🧠 Let's work it out

Solve −3x + 4 = 25.

What do you think comes next?

💡 After you move the constant, undo dividing by multiplying, or undo a fraction times x with its reciprocal.

In x/5 − 2 = 4, first add 2. Then x/5 = 6, so multiply by 5.

In (2/3)x + 1 = 9, first subtract 1. Then multiply both sides by 3/2.

🧠 Let's work it out

Solve (2/3)x + 1 = 9.

What do you think comes next?

💡 Divide both sides by the number outside the parentheses, or distribute first; both work.

In 3(x + 4) = 33, the whole group x + 4 is times 3. Divide both sides by 3 to get x + 4 = 11.

You can also distribute first: 3x + 12 = 33. Both ways give the same answer.

🧠 Let's work it out

Solve −4(x − 3) = 20.

What do you think comes next?

💡 A one-time amount plus a repeated amount makes a two-step equation.

Look for a one-time number, like a fee, and a number that repeats, like a cost per class.

Write: one-time + rate × x = total. Then solve in two steps.

If money is left over, write: start − price × x = amount left.

🧠 Let's work it out

A dance studio charges a $25 fee plus $10 per class. Ana paid $95. How many classes?

What do you think comes next?