Solving One-Step Equation Notes
This Solving One-Step Equation Calculator finds the value of a variable in an equation that needs one operation undone, and shows the working at every step. An equation stays true only while both sides are treated the same way, so whatever undoes the operation on the variable's side must be done to the other side too. Following the same pattern every time, spotting the operation, applying its inverse to both sides and then checking the answer, makes solving quick to picture and repeat.
Step-by-step method
- Set up the problem.
- Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
- Work out each side, which leaves the variable on its own.
- Check the answer by putting it back into the original equation.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
- Work out each side, which leaves the variable on its own.
- Check the answer by putting it back into the original equation.
Step 1
Step 1 - Set up the problem.
In this problem: The equation is \(x + 5 = 12\), with \(x + 5\) on the left and \(12\) on the right.
Step 2
Step 2 - Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
In this problem: The side holding \(x\) is \(x + 5\), so the operation on \(x\) is adding \(5\). The inverse of that is to subtract \(5\), and doing it to \(x + 5\) and to \(12\) keeps both sides equal.
Step 3
Step 3 - Work out each side, which leaves the variable on its own.
In this problem: On the left, \(x + 5 - 5\) leaves \(x\). On the right, \(12 - 5 = 7\). Putting the two together gives \(x = 7\).
Step 4
Step 4 - Check the answer by putting it back into the original equation.
In this problem: Putting \(7\) back in place of \(x\) turns the side holding \(x\) into \(7 + 5\), which works out to \(12\). The other side is \(12\), so both sides come to the same number.
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the problem.
- Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
- Work out each side, which leaves the variable on its own.
- Check the answer by putting it back into the original equation.
Step 1
Step 1 - Set up the problem.
In this problem: The equation is \(4x = 20\), with \(4x\) on the left and \(20\) on the right.
Step 2
Step 2 - Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
In this problem: The side holding \(x\) is \(4x\), so the operation on \(x\) is multiplying by \(4\). The inverse of that is to divide by \(4\), and doing it to \(4x\) and to \(20\) keeps both sides equal.
Step 3
Step 3 - Work out each side, which leaves the variable on its own.
In this problem: On the left, \(\frac{4x}{4}\) leaves \(x\). On the right, \(\frac{20}{4} = 5\). Putting the two together gives \(x = 5\).
Step 4
Step 4 - Check the answer by putting it back into the original equation.
In this problem: Putting \(5\) back in place of \(x\) turns the side holding \(x\) into \(4 \cdot 5\), which works out to \(20\). The other side is \(20\), so both sides come to the same number.
Final Answer
See Example 3 Hide Example 3
Problem
Approach
Step-by-step method
- Set up the problem.
- Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
- Work out each side, which leaves the variable on its own.
- Check the answer by putting it back into the original equation.
Step 1
Step 1 - Set up the problem.
In this problem: The equation is \(x - 9 = 4\), with \(x - 9\) on the left and \(4\) on the right.
Step 2
Step 2 - Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
In this problem: The side holding \(x\) is \(x - 9\), so the operation on \(x\) is subtracting \(9\). The inverse of that is to add \(9\), and doing it to \(x - 9\) and to \(4\) keeps both sides equal.
Step 3
Step 3 - Work out each side, which leaves the variable on its own.
In this problem: On the left, \(x - 9 + 9\) leaves \(x\). On the right, \(4 + 9 = 13\). Putting the two together gives \(x = 13\).
Step 4
Step 4 - Check the answer by putting it back into the original equation.
In this problem: Putting \(13\) back in place of \(x\) turns the side holding \(x\) into \(13 - 9\), which works out to \(4\). The other side is \(4\), so both sides come to the same number.
Final Answer
See Example 4 Hide Example 4
Problem
Approach
Step-by-step method
- Set up the problem.
- Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
- Work out each side, which leaves the variable on its own.
- Check the answer by putting it back into the original equation.
Step 1
Step 1 - Set up the problem.
In this problem: The equation is \(\frac{x}{5} = 7\), with \(\frac{x}{5}\) on the left and \(7\) on the right.
Step 2
Step 2 - Look at the side holding the variable, find the operation attached to it, and do the inverse operation to both sides so the equation stays balanced.
In this problem: The side holding \(x\) is \(\frac{x}{5}\), so the operation on \(x\) is dividing by \(5\). The inverse of that is to multiply by \(5\), and doing it to \(\frac{x}{5}\) and to \(7\) keeps both sides equal.
Step 3
Step 3 - Work out each side, which leaves the variable on its own.
In this problem: On the left, \(\frac{x}{5} \cdot 5\) leaves \(x\). On the right, \(7 \cdot 5 = 35\). Putting the two together gives \(x = 35\).
Step 4
Step 4 - Check the answer by putting it back into the original equation.
In this problem: Putting \(35\) back in place of \(x\) turns the side holding \(x\) into \(\frac{35}{5}\), which works out to \(7\). The other side is \(7\), so both sides come to the same number.
Final Answer