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All courses Math Foundations · MF.EQ.9 36 of 60
Write and solve a linear equation from a short verbal or contextual situation.

Write and solve an additive word-problem equation

Problem
Mia had some stickers. She got 7 more stickers and now she has 18 stickers. Write a one-step equation to represent the situation, and solve to find how many stickers she had at first.
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Hint

Let a variable stand for the number of stickers Mia had at first.

This is a start + change = total situation. She got 7 more, and 18 is the final total.

Solution walkthrough

01

Choose a variable for the starting number of stickers

\[x~=~\text{the}~\text{number}~\text{of}~\text{stickers}~\text{Mia}~\text{had}~\text{at}~\text{first}\]

The unknown is how many stickers Mia started with, so let x represent that beginning amount.

02

Write the equation from the story

\[x~+~7~=~18\]

Mia started with x stickers, then got 7 more stickers, and that made her total 18 stickers.

03

Undo the addition to solve

\[\begin{aligned} x~+~7~-~7~=~18~-~7 \\ x~=~11 \end{aligned}\]

Subtracting 7 from both sides keeps the equation balanced and isolates x.

04

State the answer in context

\[x~=~11~\text{stickers}\]

Mia had 11 stickers at first.

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Another way

  1. Check by substitution: if Mia started with 11 stickers, then 11 + 7 = 18, which matches the story.

!

Common mistake

A common mistake is writing 18 + 7 = x. The 18 stickers is the final total after she got 7 more, so the correct relationship is starting amount + 7 = 18, not 18 plus 7.