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Course: Integrated math 1 > Unit 2

Lesson 2: Linear equations with parentheses
Math
Integrated math 1
Solving equations & inequalities
Linear equations with parentheses
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Multi-step equations review

Google Classroom
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.
3x+7=133x+7−7=13−73x=63x3=63x=2
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:
3x+7=133⋅2+7=?136+7=?1313=13       Yes!

Example 2: Variables on both sides

Solve for a.
5+14a=9a−5
We need to manipulate the equation to get a by itself.
5+14a=9a−55+14a−9a=9a−5−9a5+5a=−55+5a−5=−5−55a=−105a5=−105a=−2
The answer:
a=−2
Check our work:
5+14a=9a−55+14(−2)=?9(−2)−55+(−28)=?−18−5−23=−23       Yes!
Want to learn more about solving equations with variables on both sides? Check out this video.

Example 3: Distributive property

Solve for e.
7(2e−1)−11=6+6e
We need to manipulate the equation to get e by itself.
7(2e−1)−11=6+6e14e−7−11=6+6e14e−18=6+6e14e−18−6e=6+6e−6e8e−18=68e−18+18=6+188e=248e8=248e=3
The answer:
e=3
Check our work:
7(2e−1)−11=6+6e7(2(3)−1)−11=?6+6(3)7(6−1)−11=?6+187(5)−11=?2435−11=?2424=24       Yes!
Want to learn more about solving equations with the distributive property? Check out this video.

Practice

Problem 1
Solve for b.
4b+5=1+5b
b=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want more practice? Check out these exercises:

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  • blobby green style avatar for user watermelongrin
    Posted 6 years ago. Direct link to watermelongrin's post “how did you get 5/3b?”
    how did you get 5/3b?
    (85 votes)
    Default Khan Academy avatar avatar for user
    • duskpin seed style avatar for user Amos Liberal
      Posted 3 years ago. Direct link to Amos Liberal's post “So as we can see the ques...”
      Incredible Answer
      Great Answer
      Good Answer
      So as we can see the question starts off as:
      2/3b + 5 = 20-b
      first, add +b to both sides of the equation
      (addition property of equality). Next:
      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.
      (54 votes)
  • winston default style avatar for user Colin
    Posted 2 years ago. Direct link to Colin's post “These comments be getting...”
    These comments be getting answers years later. Like bro they already progressed into High School or College, they most likely know after then.
    (57 votes)
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  • blobby green style avatar for user Ayah Khanafer
    Posted 5 years ago. Direct link to Ayah Khanafer's post “What do I do if the varia...”
    What do I do if the variable is equal to 0? How do I check my answer?
    (32 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user Polina Vitić
      Posted 5 years ago. Direct link to Polina Vitić's post “To check your answer, jus...”
      Incredible Answer
      Great Answer
      Good 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!
      (67 votes)
  • piceratops seedling style avatar for user 28nsnow
    Posted a year ago. Direct link to 28nsnow's post “Why are there documents? ...”
    Why are there documents? They could just be practices.
    (8 votes)
    Default Khan Academy avatar avatar for user
  • starky sapling style avatar for user Anna Russum
    Posted 5 years ago. Direct link to Anna Russum's post “This type of math is a li...”
    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?
    (13 votes)
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  • blobby green style avatar for user Madeline Garcia
    Posted a year ago. Direct link to Madeline Garcia's post “how is 2/3b+b =5/3b?”
    how is 2/3b+b =5/3b?
    (13 votes)
    Default Khan Academy avatar avatar for user
  • mr pants pink style avatar for user sreyar27
    Posted 7 years ago. Direct link to sreyar27's post “how do you solve an equat...”
    how do you solve an equation like 0.5(5-7x) = 8-(4x+6)
    (11 votes)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      Posted 7 years ago. Direct link to Kim Seidel's post “1) Use distributive prop...”
      Good Answer
      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.
      (18 votes)
  • stelly green style avatar for user vvkd94
    Posted a year ago. Direct link to vvkd94's post “0.5(5−7x)=8−(4x+6) how d...”
    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?
    (9 votes)
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  • blobby green style avatar for user amutsch23
    Posted a year ago. Direct link to amutsch23's post “Why do they give us probl...”
    Why do they give us problems with fractions?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      Posted a year ago. Direct link to Kim Seidel's post “Because there are many fr...”
      Good Answer
      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.
      (23 votes)
  • blobby green style avatar for user Richard Mones
    Posted 3 years ago. Direct link to Richard Mones's post “Why do you multiply by 3/...”
    Why do you multiply by 3/5 on both sides and not jut divide 15 by 5/3 in problem 2 ?
    (5 votes)
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    • mr pink green style avatar for user David Severin
      Posted 3 years ago. Direct link to David Severin's post “If you know how to divide...”
      Good Answer
      If you know how to divide fractions, they end up the same thing. You want to divide 15/(5/3), to divide fractions, you reciprocate the denominator and multiply, so you end up with 15*3/5. So if you have 5/3 x, it is easier to multiply by the reciprocal so that you do not have to go through the extra step of dividing by a fraction.
      (13 votes)