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One-Step Equations Explained
One-Step Equations Explained
Now is where we really start what most people think of when remembering Algebra 1: algebraic equations. By definition, algebraic equations are mathematical statements that express the equality of two expressions, featuring variables. To solve these equations, you will need to isolate a variable, which is a symbol (a letter such as X or Y) that represents an unknown numerical value. In this lesson, we will be solving equations that are only one step, and while it should be rather simple and easy, Algebra I (and mathematics in general) is built on what you previously learn, and this one lesson will be the true starting point of Algebra I and all of mathematics, so you must understand it well. To solve these equations, we will isolate the variable by applying the inverse of operations. For example, if the equation contains an addition symbol, we would apply the inverse operation, which is subtraction, and then subtract the number being added from both sides of the equation. This works due to the inverse operation canceling out the original operation on the side of the variable. For example, if there is an equation such as x+10=20, if you subtract the 10 from the positive 10, that would simply cancel out to 0. The table shown on the left displays the inverse operation of every operation that we will use, so refer back to it if you need assistance on the problem set. As you can see, all of the operations were also seen in the last lesson within PEMDAS, and the actual order of the operations will be needed in later lessons. Now that you have the foundational idea, let us get into some examples. In these examples, the goal of every problem is to find the value of the variable (which will be x in our case) that satisfies the equation.
Examples
Examples
1: x+12=25
As the name of the equation suggests, we will only have one step to do for each of these examples. Due to the inverse operation of addition being subtraction, we will subtract 12 from both sides of the equation, leaving x to be by itself due to the negative 12 cancelling out the positive 12, and on the other side, the difference will be 13 because 25-12 equals 13, which gives us our final answer.
Answer: x=13
2: x-33=42
In this equation, we have 33 being subtracted from x, so we will do the inverse operation, which is, of course, addition, then cancelling out the 33 on the side of x and adding to 42, giving us the sum of 75. Additionally, you can check to ensure your answer is correct by plugging the answer into the variable, creating the statement 75-33=42, which is correct.
Answer: x=75
3: x·12=96
Now we're ramping up the difficulty a bit. For this equation, x is being multiplied by 12, so we will do the inverse operation of multiplication, which is division. Yet again, the division on the side with x will cancel out the multiplication of 12, and 96 will be divided by 12 to get the quotient of 8. We can then confirm the answer by 8·12, which indeed equals 96.
Answer: x=8
4: x÷14=9
With this, we see x being divided by 14, indicating that we should use multiplication because it is the inverse operation of division. We will then multiply each side, cancelling the 14 out and then getting the answer of 126 from multiplying 9 and 14.
Answer: x=126
5: x²=64
In this equation, x is being squared, so we must do the inverse of an exponent, which is the radical symbol, aka applying the square root. Applying the square root to x² will simply make it x, and the square root of 64 is 8, which is what our answer will be.
Answer: x=8
6: √x=11
For this, we will simply do the inverse operation of square rooting something, which is squaring something, cancelling the square root applied to x out and squaring 11 to get the final answer of 121. Now, you have seen every inverse operation utilized in these 6 examples.
Answer: x=121
Problem Set
Problem Set
1: x+31=87
2: x÷7=9
3: x²=144
4: √x=5.8
5: -x=9
6: x·13=63
7: √x=8
8: x²=44
9: x-33=88
10: x·24=480
11: x+19=49
12: x²=22
Answer Key
Answer Key
1: x=56
2: x= 63
3: x= 12
4: x=33.64
5: x=-9
6: x= 4.85
7: x=64
8: x=6.63
9: x=121
10: x=20
11: x=30
12: x=4.69
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