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Course: Algebra (all content)>Unit 2

Lesson 1: Algebraic equations basics

Testing solutions to equations

In this math lesson, we learn how to solve an equation with one variable. We test different values for x to see which one satisfies the equation. By substituting x with the given options, we find the correct solution that makes both sides of the equation equal. Practice makes perfect!

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• i think all this math is hurting my head
• ugh... same here i need a math buddy to help me
• Help! When I attempted to solve for x, I got 5x is equal to 4x. Here's how I did it.
5x-3=4x+3. -3 and +3 cancel out to 0, so I am left with5x=4x.
• 5x-3=4x+3
5x=4x+6
x=6

Be careful with the signs of the constants or variables. The 3s definitely do NOT "cancel out." First I added 3 to both sides, then I subtract 4x from both sides. Hope this helps.
• So i did the equation, but im not sure i did it right.
5x-3=4x+3
+3 +3
5x = 4x+6
-4x -4x
x=6
Is this the right way to do it?
• Yes. As shown in this video, you can also check your answer by substituting it back into the original equation. Simplify both sides and make sure they are equal.

5(6)-3 = 4(6)+3
30-3 = 24+3
27 = 27
They are equal, so you have a good solution.
• He makes everything look so easy
• 7+5(x-3)=22 if x=4,5,6 and 7 which is correct and could you give me an example
• I'll do the 4 as an example:
1) Swap out "x" and replace it with the given value: 7 + 5(4 - 3) = 22
2) Follow order of operations rules (PEMDAS) to simplify the left side
-- Do the work inside the parentheses: 7 + 5(1) = 22
-- Multiply: 7 + 5 = 22
3) Are the 2 sides equal? No. This means 4 is not a solution to the equation. If the 2 sides are equal, then the number would be a solution.

Hope this helps.
• 5x-3=4x+3. -3 and +3 cancel out to 0, so I am left with5x=4x.
• -3 and +3 are on different sides of the equation. So, they do not cancel out. You must move items across the "=" by using opposite operations. So, add 3 to both sides to get: 5x=4x+6. You would then subtract 4x from both sides and end up with x=6.

If the problem was 5x+3=4x+3, then subtraction 3 would give you 5x=4x. But, don't stop there. Subtract 4x from both sides to isolate "x". You get x=0.

Hope this helps.
• Do you not work the problem so you get the answer rather than fill in possibilities? Ex:
5x-3=4x+3
5x-3+3=4x+3+3
5x=4x+6
5x-4x=4x-4x+6
×=6
• This video was about testing solutions.
-- You could be given a problem that asks you: is x=7 a solution?
-- You could have found a possible solution like you did in your work above and you want to verify that you have the correct solution.

In both of these situations, you would use the techniques shown in the video.
• how can I do it
• Did you watch the video? Did you read the other questions and responses. Multiple responses provide step-by-step instructions. Here is one that I posted 16 days ago:

If someone gives you an algebraic equation and asks if a specific value is a solution or not, here's what you do.
1) Replace each instance of the variable in the equation with the value you were given.
2) Follow order of operations rules (PEMDAS) for each side of the equation. Do the math until you have one number on both sides.
3) If the 2 sides are equal (they have the same number), then the value you were given is a solution to the equation. If the 2 sides are not equal, then you either have a math error or the given value is not a solution to the equation.

Hope this helps.
P.S. In future, look at the other info available first. Then try to ask a more specific question about what you don't understand. It will help you learn faster.
• If you don’t have choices then you can estimate.
Like 5x-3=4x+3 you can estimate to about 5.
Also, how do you simplify?