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### Course: Integrated math 1>Unit 2

Lesson 2: Linear equations with parentheses

# Multi-step equations review

To solve an equation we find the value of the variable that makes the equation true. For more complicated, fancier equations, this process can take several steps.
When solving an equation, our goal is to find the value of the variable that makes the equation true.

### Example 1: Two-step equation

Solve for $x$.
$3x+7=13$
We need to manipulate the equation to get $x$ by itself.
$\begin{array}{rl}3x+7& =13\\ \\ 3x+7-7& =13-7\\ \\ 3x& =6\\ \\ \frac{3x}{3}& =\frac{6}{3}\\ \\ x& =2\end{array}$
We call this a two-step equation because it took two steps to solve. The first step was to subtract $7$ from both sides, and the second step was to divide both sides by $3$. Want an explanation of why we do the same thing to both sides of the equation? Check out this video.
We check the solution by plugging $2$ back into the original equation:

### Example 2: Variables on both sides

Solve for $a$.
$5+14a=9a-5$
We need to manipulate the equation to get $a$ by itself.
$\begin{array}{rl}5+14a& =9a-5\\ \\ 5+14a-9a& =9a-5-9a\\ \\ 5+5a& =-5\\ \\ 5+5a-5& =-5-5\\ \\ 5a& =-10\\ \\ \frac{5a}{5}& =\frac{-10}{5}\\ \\ a& =-2\end{array}$
$a=-2$
Check our work:

### Example 3: Distributive property

Solve for $e$.
$7\left(2e-1\right)-11=6+6e$
We need to manipulate the equation to get $e$ by itself.
$\begin{array}{rl}7\left(2e-1\right)-11& =6+6e\\ \\ 14e-7-11& =6+6e\\ \\ 14e-18& =6+6e\\ \\ 14e-18-6e& =6+6e-6e\\ \\ 8e-18& =6\\ \\ 8e-18+18& =6+18\\ \\ 8e& =24\\ \\ \frac{8e}{8}& =\frac{24}{8}\\ \\ e& =3\end{array}$
$e=3$
Check our work:

## Practice

Problem 1
Solve for $b$.
$4b+5=1+5b$
$b=$

Want more practice? Check out these exercises:

## Want to join the conversation?

• how did you get 5/3b?
• So as we can see the question starts off as:
2/3b + 5 = 20-b
first, add +b to both sides of the equation
We got 5/3 by adding fractions:
2/3+1/1.
Step 1: Multiply the denominators (x/3)
Step 2: Cross multiply the numerators and denominators (2x1 and 3x1)
Step 3: Add the two products together (2x1=2, 3x1=3 therefore, add 2+3). WITHOUT touching the denominator!
Step 4: 5/3b + 5 = 20. Subtract 5 from both sides of the equation to cancel out 5.
Step 5. divide 5/3 to 15. Keep change Flip
Keep the fraction change the division sign to multiplication and flip the second fraction (example 2/3 to 3/2). So, 5/3 to 3/5 and multiply both sides of the equation, lastly, your answer is 4.
• What do I do if the variable is equal to 0? How do I check my answer?
• To check your answer, just plug 0 in for the variable.

For example, let's say you solved this equation:
9x - 1 = 5x - 1
9x - 5x = 1 - 1
4x = 0
x = 0
It looks like the variable is equal to 0.

Now, double check your answer with the original equation by replacing all the x's with 0's:
9x - 1 = 5x - 1
9(0) - 1 = 5(0) - 1
0 - 1 = 0 - 1
-1 = -1
The equation is true, so 0 is valid.

Hope this helps!
• These comments be getting answers years later. Like bro they already progressed into High School or College, they most likely know after then.
• This discussion is very important to all new comers difference in time doesn't reduce the importance of the information also it helps teachers
• am I slow if I answer something wrong?
• Why would you think that? It likely just means you need more practice. Everyone learns at their own pace.
• Why are there documents? They could just be practices.
• Some people are visual learners. For them, the videos help them learn. Other people prefer to learn by reading or looking at examples. The articles help them.
• This type of math is a little confusing because sometimes when u have a -3x you divide or subtract at least i think so i don't know why but my teacher said that and can some one explain it please?
• You divide. you can think of -3x as -3 times x, so using the opposite of multiplication(division), you can get rid of it.
• how is 2/3b+b =5/3b?
• How did 2/3b + b = 5/3b
You need a LCD to add fractions. Use LCD=3
Remember b = 1b, so 1b(3/3) = 3/3b

Now add 2/3b + 3/3b and you bet 5/3b.
Hope this helps.
• how do you solve an equation like 0.5(5-7x) = 8-(4x+6)
• 1) Use distributive property to remove the parentheses. Distribute the 0.5 and the "-"
2) On the right side, you will have 2 terms that are like terms. Combine them.
3) Move all the "x" terms to the same side of the equation
4) Move the constants to the opposite side from the x's
5) Then divide by the coefficient of "x" (the number in front of x)

See if you can solve the equation. Comment back if you get stuck with what you have done so far.
• 0.5(5−7x)=8−(4x+6)

how do we deal with 8-(4x+6)

to explain myself further; im going to multiply the 8 with 4x and the +6 as well, but how do i decide whether the result shall be negative or positive?
• You won't multipy the 8 by the 4 and the 6. You would multiply the negative sign by them making that side of the equation 8-4-6x. After that you would combine like terms giving you 4-6x and then you would solve from there.
• Why do they give us problems with fractions?
(1 vote)
• Because there are many fractions in real life, and you need to be able to work with them. Also, here you have simple fractions. In higher level math classes, the fractions be more complicated. You need to know the basics before you get to those more advanced situations.