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7th grade

Course: 7th grade > Unit 6

Lesson 5: Two-step equations with decimals and fractions
Math
7th grade
Expressions, equations, & inequalities
Two-step equations with decimals and fractions
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Two-step equations review

Google Classroom
A two-step equation is an algebraic equation that takes you two steps to solve. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.

What are two-step equations?

A two-step equation is an algebraic equation you can solve in two steps. Once you've solved it, you've found the value of the variable that makes the equation true.

Example 1

We're given an equation and asked to solve for x:
3, x, plus, 2, equals, 14
We need to manipulate the equation to get x by itself.
3x+2=143x+2−2=14−23x=123x3=123x=4\begin{aligned} 3 x + 2 &= 14 \\\\ 3 x + 2 \goldD{-2} &= 14 \goldD{-2}\\\\ 3 x &= 12\\\\ \dfrac{3 x}{\goldD 3} &= \dfrac{12}{\goldD3}\\\\ x&=4 \end{aligned}
The solution:
start color #1fab54, x, equals, 4, end color #1fab54
It's always a good idea to check our solution in the original equation to make sure we didn't make any mistakes:
3x+2=143⋅4+2=?1412+2=?1414=14    Yes!\begin{aligned} 3 x + 2 &= 14 \\\\ 3\cdot\greenD 4 + 2 &\stackrel ?= 14\\\\ 12 + 2 &\stackrel ?= 14\\\\ 14 &= 14~~~~\text{Yes!} \end{aligned}
Want to learn more about two-step equations? Check out this video.

Example 2

We're asked to solve this equation for a:
8, equals, start fraction, a, divided by, 3, end fraction, plus, 6
We need to manipulate the equation to get a by itself.
8=a3+68−6=a3+6−62=a32⋅3=a3⋅36=a\begin{aligned} 8&=\dfrac{a}{3}+6\\\\ 8\goldD{-6}&=\dfrac{a}{3}+6\goldD{-6}\\\\ 2&=\dfrac{a}{3}\\\\ 2\goldD{\cdot 3}&=\dfrac{a}{3}\goldD{\cdot 3}\\\\ 6&=a \end{aligned}
The solution:
start color #1fab54, a, equals, 6, end color #1fab54
Let's check our work (better safe than sorry!):
8=a3+68=?63+68=?2+68=8    Yes!\begin{aligned} 8&=\dfrac{a}{3}+6\\\\ 8&\stackrel ?=\dfrac{\greenD{6}}{3}+6\\\\ 8&\stackrel ?=2+6\\\\ 8&=8~~~~\text{Yes!} \end{aligned}
Want to see another example like this? Check out this video.

Practice

Problem 1
  • Current
Solve for c.
43, equals, 8, c, minus, 5
c, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Want more practice? Check out this exercise. Or try this word problem exercise.

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