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### Course: 7th grade>Unit 5

Lesson 5: Two-step equations with decimals and fractions

# Two-step equations review

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.
\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:
\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.
\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!):
\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

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

## Want to join the conversation?

• how can you solve problem like 2=(c-5+6) i do not know how to solve problems like this i need hints
• The answer is c = 1. You would first combine all the like terms in the parenthesis. The only like terms are -5 and 6. The sum of those numbers gets you 1, then by subtracting 1 from both sides you are left with c = 1. You can even check it by putting 1 in c's place: 2=(1-5+6).
• How would I solve 3^(x+3) = 9 ?
• you would multiply 3 by both x and 3....=3x+9=9
u would then minus 9 from both sides then u would get 3x=0 then u would divide both sides by and ans will be 0
• how do u solve 24= 3(n-5)
• You multiply 3 by n and then 3 by -5 and then the equation is 24=3n-15
• how can i solve more problems like this?
• how do i solve -5m/2 = 35
• how do people known the answer but not me i need hlep
• When you answer the question correct, or you press explain, then you can see how to do that question. If this doesn't work, then refresh your page.
(1 vote)
• How do you solve 8 + x/4 = -2?
• First you subtract 8 from both sides and get x/4 = -10 then multiply both sides by 4 and you get x = -40